Question

You plan to save $5,900 per year for the next 12 years. After the last deposit, you will keep the money in the account for 4 more years. The account will earn an interest rate of 6.2 percent. How much will there be in the account 16 years from today? a. $153,983.95 b. $128.0970:2 c. $25,886.92 d. $263,653.32 e. $100,702.67

Answer 1

Answer:

• b. $128.097.02

Explanation:

A constant annual investment of $5,900 for certain period is an annuity.

The equation for the future value (FV) of an annuity starting today, over t years, at an interest rate r is:

       $FV=\dfrac{(1+r)^t-1}{r}\times (1+r)}\times Annuity$

Substitute:

         $FV=\dfrac{(1+0.062)^{12}-1}{0.062}\times (1+0.062)}\times \ 5,900=\ 106,946.23$

The $106,946.23 will be kept 4 more years at the same interest rate. The future value is calculated using the formula:

          $FV=(1+r)^t\times Investment$

Substitute

          $FV=(1+0.062)^4\times \ 106,946.23=\ 128,097.02$