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Joe Beary wants to attend Riverside College. Eight years from today he will need $50,000. If Joe's bank pays 6% interest compounded
semiannually, what must Joe deposit today to have $50,000 in 8 years?

Respuesta :

Edufirst

Answer:

  • $31,158

Explanation:

Use the formula for compound interest, with semiannual compound interest rate.

      [tex]Future\text{ }Value=Deposit\times (1+APR/n)^{(n\times t)}[/tex]

For semiannual compound interest the number of periods, n, in a year is 2.

APR is the annual percentage rate, which is 6% in this problem. So, APR is 6%/2 = 0.06/2 = 0.03

Then, substitute in the formula with:

  • Future value: $50,000
  • APR/n = 0.03
  • n × t = 2 × 8 = 16

       [tex]\$50,000=Deposit\times (1+0.03)^{16}\\\\\\Deposit=\$50,000/(1.03)^{16}=\$31,158.35[/tex]

Round to the nearest dollar: $31,158.

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