To find compound interest we use:
A=P(1+nr)nt
Principal= 100,000.00
r= 4006.41=0.016025
nt= 31 quarters
A=100000(1+0.016025)31
A=163,695.3037
For Payout annuity we use the formula
P0=nrPMT(1−(1+nr)−nt
P0= Account balance at the beginning(163,695.30)
PMT= Regular withdrawal amount(1700)
r= Annual interest rate(decimal)(0.0641)
n= Number of compounds per year(12)
t= Number of years to withdraw(?)
163,695.30=120.06411700(1−(1+120.0641)−12t
1700163,695.30×0.0053=1−1.0053−12t
0.514356=1−1.0053−12t
1.0053−12t=1−0.514356
log1.0053−12t=log0.485644
−12t=log1.0053log0.485644
−12t=136.64
t=11.38years
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