Question #227756

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.

Expert's answer

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\u00d78.5302028365\u00d7(1+0.03)^{10}\\\\=\\$500\u00d78.5302028365\u00d71.34391637932\\\\=\\$5,731.939655"

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

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