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On retiring at age 68, Sugarman expects to receive $20,940 per year in Social Security payments. Assume that he receives these payments for 28 years and uses a rate of 6% per year. Find the present value of his retirement payments.

A) $20,940
B) $69,557.38
C) $146,160
D) $169,295.20

Answer :

Final answer:

The present value of Sugarman's retirement payments, given an annual payment of $20,940 for 28 years at a 6% interest rate, is calculated using the present value of an annuity formula and is approximately $169,295.20. The correct answer is option D.

Explanation:

To find the present value of Sugarman's retirement payments, we need to use the formula for the present value of an annuity. An annuity is a series of equal payments made at regular intervals over a period of time. In this case, Sugarman is expected to receive $20,940 per year for 28 years at an interest rate of 6%. The formula for the present value of an annuity is:

PV = Pmt × left (1 - (1 + r)^{-n}) / r

where:

  • PV is the present value,
  • Pmt is the annual payment,
  • r is the annual interest rate, and
  • n is the number of payments.

Plugging in the values:

PV = $20,940 × left (1 - (1 + 0.06)^{-28}) / 0.06

Calculating the above expression, we find that the present value of Sugarman's retirement payments is approximately $169,295.20.

Therefore, the correct answer to Sugarman's question is option D) $169,295.20.

Learn more about Present Value of Annuity here:

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