Question

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 m times a year. (Round your answer to the nearest cent.) S = 45,000, r = 6, t = 9, m = 2

Answer 1

Interest is compounded 2 times per year, which means it is half yearly compounding

So using PMT function in Excel we have

Periodic payment = =PMT(6%2,18,,45000) = $ 1,921.89 every half year

Here is the proof

Period for interest accumulation	Amount	FV Factor	Future Value
		(1 + 6%/2)^Period
17	$1,921.89	1.65	$   3,176.59
16	$1,921.89	1.60	$   3,084.07
15	$1,921.89	1.56	$   2,994.24
14	$1,921.89	1.51	$   2,907.03
13	$1,921.89	1.47	$   2,822.36
12	$1,921.89	1.43	$   2,740.16
11	$1,921.89	1.38	$   2,660.35
10	$1,921.89	1.34	$   2,582.86
9	$1,921.89	1.30	$   2,507.63
8	$1,921.89	1.27	$   2,434.59
7	$1,921.89	1.23	$   2,363.68
6	$1,921.89	1.19	$   2,294.84
5	$1,921.89	1.16	$   2,228.00
4	$1,921.89	1.13	$   2,163.11
3	$1,921.89	1.09	$   2,100.10
2	$1,921.89	1.06	$   2,038.93
1	$1,921.89	1.03	$   1,979.55
0	$1,921.89	1.00	$   1,921.89
			$ 45,000.00

Answer 2

SOLUTION :

Following formula will be applicable for periodic payment $R to accumulate $S in t years at interest rate of r% per year compounded m times a year ;

S = R((1 + r / (100m))^(mt) - 1) / (r / (100m))   (ANSWER).

For S = $45000 ; r = 6% ; t = 9 years ; m = 2 , we have :

=> 45000 = R ( (1 + 6 / 200)^(18) - 1 ) / (6 / 200)

=> 45000 = R * 23.4144354

=> R = 45000/23.4144354

=> R = 1921.89 ($) (ANSWER).