Question

Jake deposits 5000 at the end of each year in an investment fund earning an annual effective interest rate of 11.6%. The interest from this investment fund is paid at the end of each year into a savings account which earns an annual effective interest rate of 2.1%.

Find Jake's combined total accumulated value at the end of 16 years.

Answer 1

Statement showing interest earned every year

Year	Deposit at end of year	Interest @ 11.6%
1	5000
2	10000	5000 x 11.6%	580
3	15000	10000 x 11.6%	1160
4	20000	15000 x 11.6%	1740
5	25000	20000 x 11.6%	2320
6	30000	25000 x 11.6%	2900
7	35000	30000 x 11.6%	3480
8	40000	35000 x 11.6%	4060
9	45000	40000 x 11.6%	4640
10	50000	45000 x 11.6%	5220
11	55000	50000 x 11.6%	5800
12	60000	55000 x 11.6%	6380
13	65000	60000 x 11.6%	6960
14	70000	65000 x 11.6%	7540
15	75000	70000 x 11.6%	8120
16	80000	75000 x 11.6%	8700

Statement showing Futuve value of interest income

Year	Interest	FVIF @ 2.1%	Future value
1
2	580	1.3377	775.87
3	1160	1.3102	1519.82
4	1740	1.2832	2232.84
5	2320	1.2568	2915.89
6	2900	1.2310	3569.89
7	3480	1.2057	4195.76
8	4060	1.1809	4794.37
9	4640	1.1566	5366.59
10	5220	1.1328	5913.23
11	5800	1.1095	6435.12
12	6380	1.0867	6933.04
13	6960	1.0643	7407.75
14	7540	1.0424	7860.01
15	8120	1.0210	8290.52
16	8700	1.0000	8700.00
Total future value of interest income	76910.71

Thus Jake's combined total accumulated value at the end of 16 years = Total of principal amount + Future value of interest

= 80,000 + 76910.71

=156910.71 $