Question

Peggy Mays deposits $100 in an ordinary annuity at the end of each month in an account earning 6 percent interest compounded monthly. What is the future value of the account after 6 months

Answer 1

$610.5

Explanation:

Peggy deposits $ 100 each month in an account which gives 6% annual interest compounded after each month.

We have to calculate the future value of the account after 6 months.

Therefore, the first month's $100 will be compounded for 6 months at an interest rate of 0.5 % per month.

Again, the second month's $100 will be compounded for 5 months at an interest rate of 0.5 % per month and so on.

Hence, the final amount in the account will be

`100(1+(0.5)/(100) )^(6) + 100(1+(0.5)/(100) )^(5)+ 100(1+(0.5)/(100) )^(4) + 100(1+(0.5)/(100) )^(3)+ 100(1+(0.5)/(100) )^(2)+100(1+(0.5)/(100) )^(1)`

= 100 × 1.03 + 100 × 1.025 + 100 × 1.02 + 100 × 1.015 + 100 × 1.01 + 100 × 1.005

= $610.5 (Answer)