Answer to Question #106987 in Financial Math for Ben

Question

Steve has deposited $50,000 into an account earning 6% compounded quarterly. After 5 years, he transfers the money in his account into a RRIF earning 4.5% compounded monthly, and makes beginning-of the month withdrawals of $2000. How long can Steve make these withdrawals?

Answer 1

1. Find the accumulated amount

$FV=PV\times(1+\frac{r}{n})^{nm}=50000\times(1+\frac{0.06}{4})^{20}=\\=50000\times(1+0.015)^{20}=50 000 \times1.346855=67342.75$

2. Find the term:

Since Steve transfers money from his account to RRIF, this turns out to be annuity:

Therefore, we apply the formula:

$S=R \times \frac{(1+i)^n-1}{i}$

Therefore, we apply the formula

$\frac{S}{R}\times i+1=(1+i)^n$

Let us take the natural logarithm of this equality

$n\times \ln(1+i)=\ln(\frac{S}{R}\times i+1)$

$n=\frac{\ln(\frac{S}{R}\times i+1)}{\ln(1+i)}$

$n=\frac{\ln(\frac{67342.75}{2000}\times0.00375+1)}{\ln(1+0.00375)}$

$n=\frac{\ln(33.671375\times0.00375+1)}{\ln1.00375}$

$n=\frac{0.1188}{0.00374}=31.76$

32 months