Answer to Question #250702 in Financial Math for Bileni

Question #250702

Starting in 7 years and 9 months you want to be able to withdraw $1700 at the beginning of every month. You deposit $100 000.00 immediately and then let it grow at a rate of 6.41% compounded quarterly. For how many years will you be able to withdraw these payments?


1
Expert's answer
2021-10-25T19:13:44-0400

To find compound interest we use:

A=P(1+rn)ntA=P(1+\frac{r}{n})^{nt}

Principal== 100,000.00

r== 6.41400=0.016025\frac{6.41}{400}=0.016025

nt== 31 quarters

A=100000(1+0.016025)31A=100000(1+0.016025)^{31}

A=163,695.3037A=163,695.3037

For Payout annuity we use the formula

P0=PMT(1(1+rn)ntrnP_0= \frac{PMT(1-(1+\frac{r}{n})^{-nt}}{\frac{r}{n}}

P0=P_0= 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=1700(1(1+0.064112)12t0.064112163,695.30= \frac{1700(1-(1+\frac{0.0641}{12})^{-12t}}{\frac{0.0641}{12}}

163,695.30×0.00531700=11.005312t\frac{163,695.30×0.0053}{1700}=1-1.0053^{-12t}

0.514356=11.005312t0.514356=1-1.0053^{-12t}

1.005312t=10.5143561.0053^{-12t}=1-0.514356

log1.005312t=log0.485644log 1.0053^{-12t}=log 0.485644

12t=log0.485644log1.0053-12t=\frac{log0.485644}{log1.0053}

12t=136.64-12t=136.64

t=11.38yearst= 11.38 years



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