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
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 |
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).
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