Question

Your client wants to accumulate $2,400,000 over the next 25 years by investing the same amount at the beginning of each month. If she can expect a long-term rate of return of 9.4% compounded annually, how much must she invest each month? (Do not round intermediate calculations and round your final answer to 2 decimal places.)

The client must invest $ at the beginning of each month.

Answer 1

P=Target amount=$2,400,000

t=time in years=25 years

n=number of investments per year=12

R=rate of annual interest in %=9.4%

r=rate of interest in decimal=R/100=0.094

We know that

$monthly\;installments=\frac{rP}{n\times [1-(\frac{r}{n}+1)^{-nt}]}$

  $=\frac{0.094\times 2400000}{12\times [1-(\frac{0.094}{12}+1)^{-12\times 25}]}$

$=\frac{225600}{12\times [1-(0.007833+1)^{-300}]}$

$=\frac{18800}{ [1-(1.007833)^{-300}]}$

  $=\$20802.13$ (approx. correct upto 2 decimal places)

The client must invest $20802.13 at the beginning of each month