Question

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

Answer 1

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

Working

A B С D E 1 Years Opening balance Interest rate Intrest amount Closing balance 2 1 20 0.08 =B2*C2 =B2+D2 3 2 =E2+B2 0.08 =B3*C3 =B3+D3 4 3 =E3+20 0.08 =B4*C4 =B4+D4 5 4 =E4+20 0.08 =B5*C5 =B5+D5 6 5 =E5+20 0.08 =B6 C6 =B6+D6 76 l=E6+20 0.08 =B7*C7 =B7+D7 8 7 =E7+20 0.08 =B8C8 =B8+D8