Question

If a merchant deposits $ 1500 annually at the end of each fiscal year into a retirement account that pays interest at the rate of 8% per year compounded annually, how much money will he have in his account at the end of 25 years?

Answer 1

$ 1500 is deposited each year at the end of the year.

Interest received each year = 8 %

As the new deposit is made at the end of the year, interest will be received at 8 % on the accumulated deposit of last year (on current year deposit, interest will not be given)

No. of years = 25 years.

The deposits are shown in the table below-

On 1st year deposit, no interest will be given as the deposit is made at the end of the year.

Each year total deposit will be calculated by adding deposits of previous year + deposit in current year + interest received in current year.

Interest will be provided on the amount of last year total deposit. Current year deposit will not be taken.

For example-

In 2nd year, interest will be calculated at 8 % on last year total deposit i.e 1500

= 8 % of 1500 = 120 $

In 2nd year total deposit will become = total deposit accumulated from last year + deposit this year + interest received

= 1500 + 1500 + 120 = 3120 $

In 3rd year,

Interest will be received at 8 % on 3120 $ = 249.6 $

Total deposit at end of 3rd year = 3,120 + 1500 + 249.6 = 4869.6 $

Likewise, it is calculatd for all years and it is shown in below table-

Year	Deposited at end of each year ($)	Interest Received in current year $ @ 8 % on deposit accumulated from last years	Total Deposit (in $) = total deposit accumulated from last year + deposit this year + interest received
1	1,500	0	1500
2	1,500	120	3120
3	1,500	249.6	4869.6
4	1,500	389.568	6759.168
5	1,500	540.73344	8799.90144
6	1,500	703.9921152	11003.89356
7	1,500	880.3114844	13384.20504
8	1,500	1070.736403	15954.94144
9	1,500	1276.395315	18731.33676
10	1,500	1498.506941	21729.8437
11	1,500	1738.387496	24968.23119
12	1,500	1997.458496	28465.68969
13	1,500	2277.255175	32242.94487
14	1,500	2579.435589	36322.38045
15	1,500	2905.790436	40728.17089
16	1,500	3258.253671	45486.42456
17	1,500	3638.913965	50625.33853
18	1,500	4050.027082	56175.36561
19	1,500	4494.029249	62169.39486
20	1,500	4973.551589	68642.94645
21	1,500	5491.435716	75634.38216
22	1,500	6050.750573	83185.13274
23	1,500	6654.810619	91339.94335
24	1,500	7307.195468	100147.1388
25	1,500	8011.771106	109658.9099

Total amount accumulated at end of 25 years in account = 1,09,658.9099 $ (approx)

Hope it helps!