Question

Ms. Jones deposited ​$100 at the end of each month for 10 years into a savings account earning 6​% interest compounded monthly.​ However, she deposited an additional​ $1000 at the end of the first year. How much money was in the account at the end of the tenth ​year?

Answer 1

$1895.64

Explanation:

Given:

Principle for the first year = $100

rate of interest = 6% compounded monthly

thus,

rate per month, r = \frac{\etxtup{6}}{\textup{12}}= 0.5% = 0.005

Total time = 10 year\

Now,

for the first year

number of months, n = 12

Amount at the end of first year = Principle × ( 1 + r )ⁿ

on substituting the values, we get

Amount at the end of first year = 100 × ( 1 + 0.005 )¹²

or

Amount at the end of first year = $106.17

Therefore,

The principle amount for the consecutive years will be

= $1000 + Amount at the end of first year

= $1000 + $106.17 = $1106.17

Thus, for the rest 9 years

n = 9 × 12 = 108

Principle = $1106.17

Final amount after the end of 10th year = Principle × ( 1 + r )ⁿ

or

Final amount after the end of 10th year = $1106.17 × ( 1 + 0.005 )¹⁰⁸

or

Final amount after the end of 10th year = $1895.64