Question

Jeannie plans to deposit $6,000 in a money market sinking fund at the end of each year for the next four years. What is the amount that will accumulate by the end of the fourth and final payment if the sinking fund earns 9% interest? (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1 and PVAD of $1)

(Use appropriate factor(s) from the tables provided. Round your final answer to the nearest whole dollar amount.)

Answer 1

Solution

Following information have been provided to us,

Annual Deposits (P) = $6,000

Term (n) = 4 Years

Rate of Interest (r) = 9%, or 0.09

For determining amount accumulated at the end of 4th year, we will use the Future Value Annuity method, equation given as below,

F = P x [(1 + r)ⁿ - 1] / r

By using the values provided, we get,

F = 6000 x [(1+0.09)⁴ - 1] / 0.09

Or, F = 6000 x (1.412 - 1) / 0.09 [(1.09)⁴ = 1.412 (Approx.)]

Or, F = 6000 x (0.412 / 0.09)

Or, F = 6000 x 4.5778 [(0.412 / 0.09) = 4.5778 (Approx.)]

Or, F = 27466.80

Therefore, amount to be accumulated at the end of fourth year will be $27,467 approximately.