Question

Your grandparents put $1,200 into a saving account for you when you were born 30 years ago (on the day you were born). This account has been earning interest at a compound rate of 7%. Fill out the table below. What is its value today?  

	Amount	Interest	End of year
Year	Deposited	Earned	Balance
0	1,200.00	0.00	1,200.00
1	N/A
2	N/A
3	N/A
4	N/A
5	N/A
6	N/A
7	N/A
8	N/A
9	N/A
10	N/A
11	N/A
12	N/A
13	N/A
14	N/A
15	N/A
16	N/A
17	N/A
18	N/A
19	N/A
20	N/A
21	N/A
22	N/A
23	N/A
24	N/A
25	N/A
26	N/A
27	N/A
28	N/A
29	N/A
30	N/A

                            The amount saved should be about

Answer 1

Value of Amount at Year 0 = PV = 1200

Let number of years = n

Interest Rate = r = 7%

Value of amount after n years = FV = PV(1+r)ⁿ

Value of amount after n = 30 years = 1200*(1+0.07)³⁰ = $9134.71

End of Year balance at year n = PV(1+r)ⁿ = 1200*(1+0.07)ⁿ

Interest Earned in Year n = End of Period Balance for Year n - End of Period Balance for Year n-1

Year	Amount Deposited	Interest Earned	End of Year Balance
0	1200	0	1200.00
1	NA	84.00	1284.00
2	NA	89.88	1373.88
3	NA	96.17	1470.05
4	NA	102.90	1572.96
5	NA	110.11	1683.06
6	NA	117.81	1800.88
7	NA	126.06	1926.94
8	NA	134.89	2061.82
9	NA	144.33	2206.15
10	NA	154.43	2360.58
11	NA	165.24	2525.82
12	NA	176.81	2702.63
13	NA	189.18	2891.81
14	NA	202.43	3094.24
15	NA	216.60	3310.84
16	NA	231.76	3542.60
17	NA	247.98	3790.58
18	NA	265.34	4055.92
19	NA	283.91	4339.83
20	NA	303.79	4643.62
21	NA	325.05	4968.67
22	NA	347.81	5316.48
23	NA	372.15	5688.64
24	NA	398.20	6086.84
25	NA	426.08	6512.92
26	NA	455.90	6968.82
27	NA	487.82	7456.64
28	NA	521.96	7978.61
29	NA	558.50	8537.11
30	NA	597.60	9134.71