def timevalue(cflo, marr, base_date=0, utility=None):
"""
Computes the net value of a cashflow at time `base_date`.
Args:
cflo (TimeSeries, list of TimeSeries): cashflow.
marr (TimeSeries): Minimum atractive interest rate.
base_date (int, tuple): Time.
utility (function): utility function
Returns:
net value (float, list of floats)
>>> marr = nominal_rate([12]*5)
>>> cflo = cashflow([100]*5, spec = (0, -200))
>>> timevalue(cflo, marr) # doctest: +ELLIPSIS
103.73...
>>> timevalue(cflo, marr, 4) # doctest: +ELLIPSIS
163.22...
>>> timevalue(cflo, marr, base_date=0, utility=exp_utility_fun(200)) # doctest: +ELLIPSIS
-84.15...
>>> timevalue(cflo, marr, base_date=0, utility=log_utility_fun(210)) # doctest: +ELLIPSIS
369092793...
>>> timevalue(cflo, marr, base_date=0, utility=sqrt_utility_fun(210)) # doctest: +ELLIPSIS
2998.12...
"""
params = vars2list([cflo, marr, base_date])
cflo = params[0]
marr = params[1]
base_date = params[2]
retval = []
for xcflo, xmarr, xbase_date in zip(cflo, marr, base_date):
if not isinstance(xcflo, TimeSeries):
raise TypeError("`cflo` must be a TimeSeries")
if not isinstance(xmarr, TimeSeries):
raise TypeError("`marr` must be a TimeSeries")
verify_eq_time_range(xcflo, xmarr)
netval = 0
factor = to_discount_factor(xmarr, xbase_date)
for time, _ in enumerate(xcflo):
if utility is None:
xcflo_aux = xcflo[time]
else:
xcflo_aux = utility(xcflo[time])
netval += xcflo_aux * factor[time]
if utility is not None:
netval = utility(netval, inverse=True)
retval.append(netval)
if len(retval) == 1:
return retval[0]
return retval
def const2curr(cflo, inflation, base_date=0):
"""Converts a cashflow of constant dollars to current dollars
of the time `base_date`.
Args:
cflo (TimeSeries): A cashflow.
inflation (TimeSeries): Inflation rate.
base_date (int, tuple): base time.
Returns:
A cashflow in current money (TimeSeries)
>>> const2curr(cflo=cashflow(const_value=[100] * 5),
... inflation=nominal_rate(const_value=[10, 10, 20, 20, 20])) # doctest: +NORMALIZE_WHITESPACE
Time Series:
Start = (0,)
End = (4,)
pyr = 1
Data = (0,) 100.00
(1,) 110.00
(2,) 132.00
(3,) 158.40
(4,) 190.08
"""
params = vars2list([cflo, inflation, base_date])
cflo = params[0]
inflation = params[1]
base_date = params[2]
retval = []
for xcflo, xinflation, xbase_date in zip(cflo, inflation, base_date):
if not isinstance(xcflo, TimeSeries):
raise TypeError("cflo must be a TimeSeries object")
if not isinstance(xinflation, TimeSeries):
raise TypeError("inflation must be a TimeSeries object")
verify_eq_time_range(xcflo, xinflation)
factor = to_compound_factor(xinflation, xbase_date)
result = xcflo.copy()
for time, _ in enumerate(result):
result[time] *= factor[time]
retval.append(result)
if len(retval) == 1:
return retval[0]
return retval
def curr2const(cflo, inflation, base_date=0):
"""Converts a cashflow of current dollars to constant dollars of
the time `t0`.
Args:
cflo (list, Cashflow): A cashflow.
inflation_rate (float, Rate): Inflation rate.
t0 (int): base time.
Returns:
A cashflow in constant dollars
>>> curr2const(cflo=cashflow(const_value=[100] * 5),
... inflation=nominal_rate(const_value=[10, 10, 20, 20, 20])) # doctest: +NORMALIZE_WHITESPACE
Time Series:
Start = (0,)
End = (4,)
pyr = 1
Data = (0,) 100.00
(1,) 90.91
(2,) 75.76
(3,) 63.13
(4,) 52.61
"""
params = vars2list([cflo, inflation, base_date])
cflo = params[0]
inflation = params[1]
base_date = params[2]
retval = []
for xcflo, xinflation, xbase_date in zip(cflo, inflation, base_date):
if not isinstance(xcflo, TimeSeries):
raise TypeError("cflo must be a TimeSeries object")
if not isinstance(xinflation, TimeSeries):
raise TypeError("inflation must be a TimeSeries object")
verify_eq_time_range(xcflo, xinflation)
factor = to_discount_factor(xinflation, xbase_date)
result = xcflo.copy()
for time, _ in enumerate(result):
result[time] *= factor[time]
retval.append(result)
if len(retval) == 1:
return retval[0]
return retval
def currency_conversion(cflo, exchange_rate=1, devaluation=None, base_date=0):
"""Converts a cashflow of dollars to another currency.
Args:
cflo (TimeSeries): A cashflow.
exchange_rate (float): Exchange rate at time `base_date`.
devaluaton (TimeSeries): Devaluation rate.
base_date (int): Time.
Returns:
A cashflow in other currency.
"""
params = vars2list([cflo, exchange_rate, devaluation, base_date])
cflo = params[0]
exchange_rate = params[1]
devaluation = params[2]
base_date = params[3]
retval = []
for xcflo, xexchange_rate, xdevaluation, xbase_date in zip(
cflo, exchange_rate, devaluation, base_date):
if not isinstance(xcflo, TimeSeries):
raise TypeError("`cashflow` must be a TimeSeries")
if xdevaluation is None:
result = xcflo.copy()
for time, _ in enumerate(result):
result[time] *= xexchange_rate
else:
if not isinstance(xdevaluation, TimeSeries):
raise TypeError("`devaluation` must be a TimeSeries")
verify_eq_time_range(xcflo, xdevaluation)
factor = to_compound_factor(xdevaluation, xbase_date)
result = xcflo.copy()
for time, _ in enumerate(result):
result[time] *= xexchange_rate * factor[time]
retval.append(result)
if len(retval) == 1:
return retval[0]
return retval
def after_tax_cashflow(cflo, tax_rate):
"""Computes the after cashflow for a tax rate. Taxes are not computed
for negative values in the cashflow.
Args:
cflo (TimeSeries): generic cashflow.
tax_rate (TimeSeries): income tax rate.
Returns:
TimeSeries objects with taxed values
>>> cflo = cashflow(const_value=[100] * 5, spec=(0, -100))
>>> tax_rate = nominal_rate(const_value=[10] * 5)
>>> after_tax_cashflow(cflo=cflo, tax_rate=tax_rate) # doctest: +NORMALIZE_WHITESPACE
Time Series:
Start = (0,)
End = (4,)
pyr = 1
Data = (0,) 0.00
(1,)-(4,) [4] 10.00
"""
params = vars2list([cflo, tax_rate])
cflo = params[0]
tax_rate = params[1]
retval = []
for xcflo, xtax_rate in zip(cflo, tax_rate):
if not isinstance(xcflo, TimeSeries):
raise TypeError("cashflow must be a TimeSeries")
verify_eq_time_range(xcflo, xtax_rate)
result = xcflo.copy()
for time, _ in enumerate(xcflo):
if result[time] > 0:
result[time] *= xtax_rate[time] / 100
else:
result[time] = 0
retval.append(result)
if len(retval) == 1:
return retval[0]
return retval
def depreciation_sl(costs, life, salvalue=None, delay=None, noprint=True):
"""Computes the depreciation of an asset using straight line depreciation
method.
Args:
cost (TimeSeries): the cost per period of the assets.
life (TimeSeries): number of depreciation periods for the asset.
salvalue(TimeSeries): salvage value as a percentage of cost.
noprint (bool): when True, the procedure prints a depreciation table.
Returns:
depreciation, accum_depreciation (TimeSeries, TimeSeries).
"""
verify_eq_time_range(costs, life)
if salvalue is not None:
verify_eq_time_range(costs, salvalue)
else:
salvalue = [0] * len(costs)
if delay is not None:
verify_eq_time_range(costs, delay)
else:
delay = [0] * len(costs)
depr = [0] * len(costs)
adepr = [0] * len(costs)
begbook = [0] * len(costs)
endbook = [0] * len(costs)
for index, _ in enumerate(costs):
if costs[index] == 0:
continue
if delay[index] == 0:
ValueError('Depreciation with delay 0')
xdepr = [(costs[index] *
(100 - salvalue[index]) / 100) / life[index]] * life[index]
for time in range(life[index]):
if index + time + delay[index] + 1 < len(costs):
depr[index + time + delay[index] + 1] += xdepr[time]
else:
break
for time, _ in enumerate(depr):
if time > 0:
adepr[time] = adepr[time - 1] + depr[time]
else:
adepr[time] = depr[time]
for time, _ in enumerate(depr):
if time > 0:
begbook[time] = endbook[time - 1]
endbook[time] = begbook[time] - depr[time] + costs[time]
if noprint is True:
retval = costs.copy()
for index, _ in enumerate(costs):
retval[index] = depr[index]
return retval
print_depr(depr, adepr, costs, begbook, endbook)
def benefit_cost_ratio(cflo, marr, base_date=0):
"""
Computes a benefit cost ratio at time `base_date` of a cashflow.
Args:
rate (int float, Rate): Minimum atractive interest rate.
cashflow (cashflow, list): cashflow.
base_date (int, list): Time.
Returns:
(float) net present value.
"""
params = vars2list([marr, cflo, base_date])
marr = params[0]
cflo = params[1]
base_date = params[2]
retval = []
for xmarr, xcflo, xbase_date in zip(marr, cflo, base_date):
verify_eq_time_range(xcflo, xmarr)
num = 0
den = 0
num = xcflo.copy()
den = xcflo.copy()
for time, _ in enumerate(xcflo):
if xcflo[time] >= 0.0:
den[time] = 0
else:
num[time] = 0
retval.append(-timevalue(num, xmarr, xbase_date) /
timevalue(den, xmarr, xbase_date))
if len(retval) == 1:
return retval[0]
return retval
def depreciation_soyd(costs, life, salvalue=None, delay=None, noprint=True):
"""Computes the depreciation of an asset using the sum-of-year's-digits
method.
Args:
cost (TimeSeries): the cost per period of the assets.
life (TimeSeries): number of depreciation periods for the asset.
salvalue(TimeSeries): salvage value as a percentage of cost.
noprint (bool): when True, the procedure prints a depreciation table.
Returns:
A tuple (dep, accum) of lists (tuple): depreciation per period and accumulated depreciation per period
"""
verify_eq_time_range(costs, life)
if salvalue is not None:
verify_eq_time_range(costs, salvalue)
else:
salvalue = [0] * len(costs)
if delay is not None:
verify_eq_time_range(costs, delay)
else:
delay = [0] * len(costs)
depr = [0] * len(costs)
adepr = [0] * len(costs)
begbook = [0] * len(costs)
endbook = [0] * len(costs)
for index, _ in enumerate(costs):
sumdig = life[index] * (life[index] + 1) / 2
xdepr = [(costs[index] * (100 - salvalue[index]) / 100) *
(life[index] - time) / sumdig for time in range(life[index])]
for time in range(life[index]):
if index + time + delay[index] + 1 < len(costs):
depr[index + time + delay[index] + 1] += xdepr[time]
else:
break
for time, _ in enumerate(depr):
if time > 0:
adepr[time] = adepr[time - 1] + depr[time]
else:
adepr[time] = depr[time]
for time, _ in enumerate(depr):
if time > 0:
begbook[time] = endbook[time - 1]
endbook[time] = begbook[time] - depr[time] + costs[time]
if noprint is True:
retval = costs.copy()
for index, _ in enumerate(costs):
retval[index] = depr[index]
return retval
print_depr(depr, adepr, costs, begbook, endbook)
def fixed_ppal_loan(amount,
nrate,
grace=0,
dispoints=0,
orgpoints=0,
prepmt=None,
balloonpmt=None):
"""Loan with fixed principal payment.
"""
#pylint: disable-msg=too-many-arguments
if not isinstance(nrate, TimeSeries):
TypeError('nrate must be a TimeSeries object.')
if prepmt is None:
prepmt = cashflow(start=nrate.start, end=nrate.end, pyr=nrate.pyr)
else:
verify_eq_time_range(nrate, prepmt)
if balloonpmt is None:
balloonpmt = cashflow(start=nrate.start, end=nrate.end, pyr=nrate.pyr)
else:
verify_eq_time_range(nrate, balloonpmt)
# present value of the balloon payments
balloonpv = sum(balloonpmt)
life = len(nrate) - grace - 1
begppalbal = TimeSeries(start=nrate.start, end=nrate.end, pyr=nrate.pyr)
intpmt = TimeSeries(start=nrate.start, end=nrate.end, pyr=nrate.pyr)
ppalpmt = TimeSeries(start=nrate.start, end=nrate.end, pyr=nrate.pyr)
totpmt = TimeSeries(start=nrate.start, end=nrate.end, pyr=nrate.pyr)
endppalbal = TimeSeries(start=nrate.start, end=nrate.end, pyr=nrate.pyr)
pmt = (amount - balloonpv) / life # periodic ppal payment
# balance calculation
for time in range(grace + life + 1):
if time == 0:
begppalbal[time] = 0
endppalbal[time] = amount - prepmt[time]
totpmt[time] = amount * (dispoints + orgpoints)
intpmt[time] = amount * dispoints
else:
begppalbal[time] = endppalbal[time - 1]
intpmt[time] = begppalbal[time] * nrate[time] / nrate.pyr / float(
100)
if time <= grace:
ppalpmt[time] = prepmt[time] + balloonpmt[time]
else:
ppalpmt[time] = pmt + prepmt[time] + balloonpmt[time]
totpmt[time] = intpmt[time] + ppalpmt[time]
endppalbal[time] = begppalbal[time] - ppalpmt[time]
if endppalbal[time] < 0:
totpmt[time] = begppalbal[time] + intpmt[time]
ppalpmt[time] = begppalbal[time]
endppalbal[time] = begppalbal[time] - ppalpmt[time]
prepmt[time] = 0
pmt = 0
## resuls
result = Loan()
result.life = life
result.nrate = nrate
result.grace = grace
result.amount = amount
result.begppalbal = begppalbal
result.totpmt = totpmt
result.intpmt = intpmt
result.ppalpmt = ppalpmt
result.endppalbal = endppalbal
return result
def buydown_loan(amount,
nrate,
grace=0,
dispoints=0,
orgpoints=0,
prepmt=None):
"""
Buydown loan
"""
if not isinstance(nrate, TimeSeries):
TypeError('nrate must be a TimeSeries object.')
if prepmt is None:
prepmt = cashflow(start=nrate.start, end=nrate.end, pyr=nrate.pyr)
else:
verify_eq_time_range(nrate, prepmt)
life = len(nrate) - grace - 1
begppalbal = TimeSeries(start=nrate.start, end=nrate.end, pyr=nrate.pyr)
intpmt = TimeSeries(start=nrate.start, end=nrate.end, pyr=nrate.pyr)
ppalpmt = TimeSeries(start=nrate.start, end=nrate.end, pyr=nrate.pyr)
totpmt = TimeSeries(start=nrate.start, end=nrate.end, pyr=nrate.pyr)
endppalbal = TimeSeries(start=nrate.start, end=nrate.end, pyr=nrate.pyr)
if prepmt is None:
prepmt = cashflow(start=nrate.start, end=nrate.end, pyr=nrate.pyr)
else:
verify_eq_time_range(nrate, prepmt)
##
## balance calculation
##
for time in range(grace + life + 1):
if time == 0:
#
begppalbal[time] = amount
endppalbal[time] = amount
totpmt[time] = amount * (dispoints + orgpoints)
intpmt[time] = amount * dispoints
#
else:
#
# periodic payment per period
#
if time <= grace:
begppalbal[time] = endppalbal[time - 1]
intpmt[time] = begppalbal[time] * nrate[time] / nrate.pyr / 100
totpmt[time] = intpmt[time]
endppalbal[time] = begppalbal[time]
else:
pmt = -pvpmt(nrate=nrate[time],
nper=grace + life - time + 1,
pval=endppalbal[time - 1],
pmt=None,
pyr=nrate.pyr)
totpmt[time] = pmt + prepmt[time]
# balance
begppalbal[time] = endppalbal[time - 1]
intpmt[time] = begppalbal[time] * nrate[time] / nrate.pyr / 100
ppalpmt[time] = totpmt[time] - intpmt[time]
endppalbal[time] = begppalbal[time] - ppalpmt[time]
## resuls
result = Loan()
result.nrate = nrate
result.life = life
result.grace = grace
result.amount = amount
result.begppalbal = begppalbal
result.totpmt = totpmt
result.intpmt = intpmt
result.ppalpmt = ppalpmt
result.endppalbal = endppalbal
return result
def fixed_rate_loan(amount,
nrate,
life,
start,
pyr=1,
grace=0,
dispoints=0,
orgpoints=0,
prepmt=None,
balloonpmt=None):
"""Fixed rate loan
"""
if not isinstance(float(nrate), float):
TypeError('nrate must be a float.')
nrate = nominal_rate(const_value=nrate,
start=start,
nper=life + grace + 1,
pyr=pyr)
if prepmt is None:
prepmt = cashflow(start=nrate.start, end=nrate.end, pyr=nrate.pyr)
else:
verify_eq_time_range(nrate, prepmt)
if balloonpmt is None:
balloonpmt = cashflow(start=nrate.start, end=nrate.end, pyr=nrate.pyr)
else:
verify_eq_time_range(nrate, balloonpmt)
# present value of the balloon payments
if balloonpmt is not None:
balloonpv = timevalue(cflo=balloonpmt, marr=nrate, base_date=grace)
else:
balloonpv = 0
pmt = pvpmt(pmt=None,
pval=-amount + balloonpv,
nrate=nrate[0],
nper=len(nrate) - 1,
pyr=nrate.pyr)
pmts = cashflow(start=nrate.start, end=nrate.end, pyr=nrate.pyr)
for time in range(1, life + 1):
pmts[grace + time] = pmt
# balance
begppalbal = TimeSeries(start=nrate.start, end=nrate.end, pyr=nrate.pyr)
intpmt = TimeSeries(start=nrate.start, end=nrate.end, pyr=nrate.pyr)
ppalpmt = TimeSeries(start=nrate.start, end=nrate.end, pyr=nrate.pyr)
totpmt = TimeSeries(start=nrate.start, end=nrate.end, pyr=nrate.pyr)
endppalbal = TimeSeries(start=nrate.start, end=nrate.end, pyr=nrate.pyr)
# payments per period
for time, _ in enumerate(totpmt):
totpmt[time] = pmts[time] + balloonpmt[time] + prepmt[time]
# balance calculation
for time in range(grace + life + 1):
if time == 0:
begppalbal[0] = amount
endppalbal[0] = amount
totpmt[time] = amount * (dispoints + orgpoints)
intpmt[time] = amount * dispoints
else:
begppalbal[time] = endppalbal[time - 1]
if time <= grace:
intpmt[time] = begppalbal[time] * nrate[time] / nrate.pyr / 100
totpmt[time] = intpmt[time]
endppalbal[time] = begppalbal[time]
else:
intpmt[time] = begppalbal[time] * nrate[time] / nrate.pyr / 100
ppalpmt[time] = totpmt[time] - intpmt[time]
if ppalpmt[time] < 0:
capint = -ppalpmt[time]
ppalpmt[time] = 0
else:
capint = 0
endppalbal[time] = begppalbal[time] - ppalpmt[time] + capint
if endppalbal[time] < 0:
totpmt[time] = begppalbal[time] + intpmt[time]
ppalpmt[time] = begppalbal[time]
endppalbal[time] = begppalbal[time] - ppalpmt[time]
pmts[time] = 0
prepmt[time] = 0
result = Loan()
result.life = life
result.nrate = nrate
result.grace = grace
result.amount = amount
result.begppalbal = begppalbal
result.totpmt = totpmt
result.intpmt = intpmt
result.ppalpmt = ppalpmt
result.endppalbal = endppalbal
return result
def depreciation_db(costs,
life,
salvalue=None,
factor=1,
convert_to_sl=True,
delay=None,
noprint=True):
"""Computes the depreciation of an asset using the declining balance
method.
Args:
ccost (TimeSeries): the cost per period of the assets.
life (TimeSeries): number of depreciation periods for the asset.
salvalue(TimeSeries): salvage value as a percentage of cost.
factor (float): acelerating factor for depreciation.
convert_to_sl (bool): converts to straight line method?
noprint (bool): when True, the procedure prints a depreciation table.
Returns:
A tuple (dep, accum) of lists (tuple): depreciation per period and accumulated depreciation per period
"""
verify_eq_time_range(costs, life)
if salvalue is not None:
verify_eq_time_range(costs, salvalue)
else:
salvalue = [0] * len(costs)
if delay is not None:
verify_eq_time_range(costs, delay)
else:
delay = [0] * len(costs)
if not isinstance(factor, (int, float)):
raise TypeError('Invalid type for `factor`')
if not isinstance(convert_to_sl, bool):
raise TypeError('Invalid type for `convert_to_sl`')
depr = [0] * len(costs)
adepr = [0] * len(costs)
begbook = [0] * len(costs)
endbook = [0] * len(costs)
for index, _ in enumerate(costs):
if costs[index] == 0:
continue
xfactor = factor / life[index]
rem_cost = costs[index]
xdepr = [0] * life[index]
sl_depr = (costs[index] - salvalue[index]) / life[index]
for time in range(life[index]):
xdepr[time] = rem_cost * xfactor
if convert_to_sl is True and xdepr[time] < sl_depr:
xdepr[time] = sl_depr
rem_cost -= xdepr[time]
if rem_cost < salvalue[index]:
rem_cost += xdepr[time]
xdepr[time] = rem_cost - salvalue[index]
rem_cost = salvalue[index]
for time in range(life[index]):
if index + time + delay[index] + 1 < len(costs):
depr[index + time + delay[index] + 1] += xdepr[time]
else:
break
for time, _ in enumerate(depr):
if time > 0:
adepr[time] = adepr[time - 1] + depr[time]
else:
adepr[time] = depr[time]
for time, _ in enumerate(depr):
if time > 0:
begbook[time] = endbook[time - 1]
endbook[time] = begbook[time] - depr[time] + costs[time]
if noprint is True:
retval = costs.copy()
for index, _ in enumerate(costs):
retval[index] = depr[index]
return retval
print_depr(depr, adepr, costs, begbook, endbook)
def savings(deposits, rate, initbal=0, noprint=True):
"""
Computes the final balance for a savings account with arbitrary deposits and
withdrawls and variable interset rate.
Args:
deposits (TimeSeries): deposits to the account.
rate (TimeSeries): interest rate paid by the account.
initbal (float): initial balance of the account.
noprint (bool): prints summary report?
Return:
interest, end_balance (TimeSeries, TimeSeries)
"""
verify_eq_time_range(deposits, rate)
begbal = deposits.copy()
interest = deposits.copy()
endbal = deposits.copy()
for time, _ in enumerate(deposits):
if time == 0:
begbal[0] = initbal
interest[0] = begbal[0] * rate[0] / 100 / rate.pyr
endbal[0] = begbal[0] + deposits[0] + interest[0]
else:
begbal[time] = endbal[time - 1]
interest[time] = begbal[time] * rate[time] / 100 / rate.pyr
if deposits[time] < 0 and -deposits[time] > begbal[
time] + interest[time]:
deposits[time] = -(begbal[time] + interest[time])
endbal[time] = begbal[time] + deposits[time] + interest[time]
if noprint is True:
return (interest, endbal)
len_timeid = len(deposits.end.__repr__())
len_number = max(len('{:1.2f}'.format(endbal[-1])),
len('{:1.2f}'.format(begbal[0])), 9)
fmt_timeid = '{:<' + '{:d}'.format(len_timeid) + 's}'
fmt_number = ' {:' + '{:d}'.format(len_number) + '.2f}'
fmt_header = ' {:>' + '{:d}'.format(len_number) + 's}'
if deposits.pyr == 1:
xmajor, = deposits.start
xminor = 0
else:
xmajor, xminor = deposits.start
txt = []
header = fmt_timeid.format('t')
header += fmt_header.format('Beginning')
header += fmt_header.format('Deposit')
header += fmt_header.format('Earned')
header += fmt_header.format('Ending')
txt.append(header)
header = fmt_timeid.format('')
header += fmt_header.format('Balance')
header += fmt_header.format('')
header += fmt_header.format('Interest')
header += fmt_header.format('Balance')
txt.append(header)
txt.append('-' * len_timeid + '-----' + '-' * len_number * 4)
for time, _ in enumerate(deposits):
if deposits.pyr == 1:
timeid = (xmajor, )
else:
timeid = (xmajor, xminor)
fmt = fmt_timeid + fmt_number * 4
txt.append(
fmt.format(timeid.__repr__(), begbal[time], deposits[time],
interest[time], endbal[time]))
if deposits.pyr == 1:
xmajor += 1
else:
xminor += 1
if xminor == deposits.pyr:
xminor = 0
xmajor += 1
print('\n'.join(txt))