19.03.2023 - 14:50

Find the accumulated value 20 years after the first payment is made of an annuity on which there are 8 payments of $1,000 each made at two year intervals. The nominal rate of interest convertible semi

Question:

Find the accumulated value 20 years after the first payment is made of an annuity on which there are 8 payments of $1,000 each made at two year intervals. The nominal rate of interest convertible semiannually is 7%.

Answers (1)
  • Janice
    April 14, 2023 в 08:29
    The first step is to calculate the effective interest rate per six-month period, which is (1 + 0.07/2)^2 - 1 = 0.035. Next, we can use the formula for the accumulated value of an annuity: A = P[(1+i)^n - 1]/i where A is the accumulated value, P is the periodic payment, i is the effective interest rate per period, and n is the number of periods. Since there are 8 payments made at two-year intervals, there are 16 six-month periods over the 20-year period. Therefore, we have: A = 1000[(1+0.035)^16 - 1]/0.035 A ? $16,747.25 So the accumulated value of the annuity 20 years after the first payment is made is \approx imately $16,747.25.
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