You invest $20 at the beginning of each year for the next 7 years at the annual rate of 8%. How much interest results from compounding (in dollars)?
A. Below 5
B. Between 5 and 10
C. Between 10 and 15
D. Between 15 and 28
E. Between 28 and 42
F. Between 42 and 52
G. Between 52 and 62
H. Between 62 and 85
I. Above 85
Sol:
Annual payment (P) = $20
Period (n) = 7 years
Annual rate (r) = 8%
To determine interest amount results from compounding:
Future value (FVA Due) = P x [(1+r)^n-1] x (1 + r) / r
FV = 20 x [(1 + 8%)^7 -1] x (1 + 8%) / 8%
FV = 20 x [(1.08)^7 -1 x 1.08] / 0.08
FV = 20 x 9.636628 = $192.73
Total investment = 20 x 7 = $140
Interest amount = FV - Total investment
Interest amount = )$192.73 - $140) = $52.73
Therefore interest amount results from compounding = $52.73
Answer will be G. Between 52 and 62
Future value can also be determined in excel as:
Years | Opening balance | Interest rate | Interest amount | Closing balance |
1 | 20.00 | 8% | 1.60 | 21.60 |
2 | 41.60 | 8% | 3.33 | 44.93 |
3 | 64.93 | 8% | 5.19 | 70.12 |
4 | 90.12 | 8% | 7.21 | 97.33 |
5 | 117.33 | 8% | 9.39 | 126.72 |
6 | 146.72 | 8% | 11.74 | 158.46 |
7 | 178.46 | 8% | 14.28 | 192.73 |
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