Find the periodic payment R required to accumulate a sum of S dollars over t years with interest earned at the rate of r%/year compounded

Question

Find the periodic payment R required to accumulate a sum of  S dollars over tyears with interest earned at the rate of r%/year compounded m times a year. (Round your answer to the nearest cent.)

S = 40,000, r = 4, t = 10, m = 12

Answer 1

Hi Kibiie,

This question is missing one assumption: is this periodic payment an ordinary annuity or an annuity due?

Ordinary (or Regular) Annuity: periodic payment is made towards the end of the month. 1/31, 2/28, 3/31, etc.

Annuity Due: periodic payment is made on the 1st of the month, i.e. 1/1, 2/1, 3/1, etc.

In other words: for an Annuity Due, the first payment made will compound interest in the same month the payment is made, while Ordinary Annuities compound interest in the ensuing month. Please let me know if I need to clarify ordinary annuity vs. annuity due. Since it's not clarified in your question, it's most likely assumed to be an Ordinary Annuity, however, I will provide the answer for both scenarios:

Ordinary/Regular Annuity Payment

PMT = FV / ((((1+(R/M))^(N*M))-1)/(R/M))

FV = 40,000

R = 4%

N = 10 Years

M = 12 months compounded per year

PMT = 40,000 / ((((1+(.04/12))^(10*12))-1)/(.04/12))

PMT = 40,000 / (((1.0333^120)-1)/.0333)

PMT = 40,000 / 147.25

PMT = $271.65 FINAL ANSWER

Annuity Due Payment

PMT = FV / (((((1+(R/M))^(N*M))-1)/(R/M))+(1+R/M))

FV = 40,000

R = 4%

N = 10 Years

M = 12 months compounded per year

PMT = 40,000 / (((((1+(.04/12))^(10*12))-1)/(.04/12))(1+(.04/12)))

PMT = 40,000 / ((((1.0333^120)-1)/.0333)(1.0333))

PMT = 40,000 / 147.74

PMT = $270.74 FINAL ANSWER