Question

Your client wants to accumulate $1,200,000 over the next 20 years by investing the same amount at the beginning of each month. If she can expect a long-term rate of return of 8.2% 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

Future Value of annuty = P* [( 1 +R)^N - 1] / R * ( 1 +R)

Where, P = payment per period

N = Number of periods

R = Rate of interest per period

1200000 = P * [( 1 + (8.2%/12))^20*12) - 1] / (8.2%/12) * ( 1 + 8.2%/12)

1200000 = P * [( 1 + 0.683333%)^240 - 1) / 0.683333%] * (1.0068333333)

1200000 = P * (5.12649027583 - 1)/ 0.00683333 * ( 1.0068333333)

1200000 = P * 603.876920305 * ( 1.0068333333)

P = 1200000 / 608.003412574

P = 1973.6731

So, The monthly payment is 1973.6731