Question

Compute the amount Amanda m u st deposit in an account today so that sh e can pay herself $450 p er mont h for the next nin e years if her opportunity cost rate is 8.4 percent compounded monthly. How much must Amanda dep osit today if sh e wants to p ay herself at the beginnin g of each month?

Answer 1

Amanda wants to have $450 per month for 9 years. Since the money would be in equal amount this is an annuity. Thus, to find the amount to be deposited we calculate for present value of annuity due (beginning of the period)

Present Value (PV) of Annuity Due = PMT × ((1 – (1 + r)⁻ⁿ) / r) * (1 + r)

where, PMT = Periodic cash payment = 450

r = Interest rate per period = 8.4%/12 = 0.007

n = Total number of periods = 9*12 = 108

= 450 * ((1 - (1 + 0.007)⁻¹⁰⁸) / 0.007) * 1.007

= 450 * ((1 - 0.47)/0.007) * 1.007

= 34,309.93

= $34,309.93

Explanation: