In: Finance
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?
$ 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!