Question

10. Each year for 5 years, a deposit is made for $500.00 into a fund paying 6 percent interest per year. How much will be accumulated in the fund at t = 5, and at t = 10?

Answer 1

Given -

* Annuity Payment (P) = $500

* Rate (r) = 6% = 0.06

* Time (n) = 5 years

We can calculate the amount accumulated after 5 years using the formula for future value of annuity.

Future Value of Annuity = P * [ ( 1 + r )ⁿ - 1 / r ]

Future Value of Annuity = 500 * [ ( 1 + 0.06 )⁵ - 1 / 0.06 ]

Future Value of Annuity = $2,818.55

Therefore, the amount accumulated after 5 years will be $2,818.55

Further, there is no annual payment after year 5. Therefore, the amount accumulated after 10 years is the future value of the amount accumulated after 5 years.

Future Value = Present Value * ( 1 + r )^t

Or,

Future Value = 2818.55 * ( 1 + 0.06 )5

Or,

Future Value = $3,771.86

Therefore, the amount accumulated after 10 years will be $3,771.86