Question

Find the periodic payments PMT necessary to accumulate the given amount in an annuity account. (Assume end-of-period deposits and compounding at the same intervals as deposits. Round your answer to the nearest cent.)

1) $20,000 in a fund paying 6% per year, with monthly payments for 10 years

PMT = $

2) $50,000 in a fund paying 5% per year, with monthly payments for 5 years, if the fund contains $10,000 at the start

PMT = $

Answer 1

1). Given that,

Amount needed in t = 10 years is FV = $20000

interest rate r = 6% per year compounded monthly

compounding frequency n = 12

So, monthly deposits can be calculated using FV formula of annuity

PMT = FV*(r/n)/((1+r/n)^(n*t) - 1) = 20000*(0.06/12)/((1+0.06/12)^(12*10) -1) = $122.04

So, PMT = $122.04

2). Given that,

Amount needed in t = 5 years is FV = $50000

interest rate r = 5% per year compounded monthly

compounding frequency n = 12

fund already has PV = $10000

So, monthly deposits can be calculated using FV formula of annuity

PMT = FV*(r/n)/((1+r/n)^(n*t) - 1) - PV(r/n)/(1 - (1+r/n)^(-n*t))

=> PMT = 50000*(0.05/12)/((1+0.05/12)^(12*5) -1) - 10000*(0.05/12)/(1 - (1+0.05/12)^(-12*5)) = $546.52

So, PMT = $546.52