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Lubov Fominskaja [6]
3 years ago
14

Joe Beary wants to attend Riverside College. Eight years from today he will need $50,000. If Joe's bank pays 6% interest compoun

ded
semiannually, what must Joe deposit today to have $50,000 in 8 years?
Business
1 answer:
dexar [7]3 years ago
6 0

Answer:

  • <u><em>$31,158</em></u>

<u><em></em></u>

Explanation:

Use the formula for compound interest, with <em>semiannual</em> compound interest rate.

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

For<em> semiannual </em>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

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

Round to the nearest dollar: $31,158.

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