Question

(15) You have $200,000 in an account earning 6% compounded monthly. 6 years from now you want to make quarterly deposits for 9 years so that when you retire 15 years from now you will have accumulated $750,000. How much should your deposits be to achieve that goal?

Answer 1

The future value of $200,000 in 6 years:

n = 6 * 12 = 72 months

r = 6%/12 = 0.005

FV = PV * (1 + r)^n

FV = 200,000 * (1 + 0.005)^72

FV = $286,408.855698331

Now with this as PV, we need to find the quarterly payments for 9 years such that FV = $750,000 in 15 years

Number of quarterly payments, N = 9 * 4 = 36

Effective quarterly rate = (1 + 0.005)^4 - 1 = 0.02015050062

I/Y = 2.015050062

PV = -286,408.855698331

FV = 750,000

CPT PMT

PMT = -3,119.116835

Quarterly deposits should be $3,119.116835 to achieve our goal