Question

Mary decided to begin saving towards the purchase of a new car in 5 years. If Mary put $500 at the end of each of each 6-month period for 5 years and the account paid 6 percent compounded semiannually. How much will Mary accumulate after 5 years? Note: Mary is only making 10 payments, with first payment is six months from today and the interest is compounded semiannually.

Answer 1

Compute the semi-annual interest rate, using the equation as shown below:

Semi annual rate$=\frac{Annual rate}{2}$

$=\frac{6\%}{2}\\=3\%$

Hence, the semi-annual interest rate is 3%.

Compute the present value annuity factor (PVIFA), using the equation as shown below:

$PVIFA=\frac{1-(1+Rate)^{-Time}}{Rate}\\=\frac{1-(1+0.03)^{-10}}{3\%}\\=8.5302028365$

Hence, the present value annuity factor is 8.5302028365.

Compute the value of deposits after 5 years, using the equation as shown below:

Future value=Semi annual deposits×PVIFA×(1+Rate)^Time

$=\$500×8.5302028365×(1+0.03)^{10}\\=\$500×8.5302028365×1.34391637932\\=\$5,731.939655$

Hence, the value of deposits after 5 years will be $5,731.94.