Present Value of an Annuity Determine the present value of $200,000 to be receiv

Question

Present Value of an Annuity Determine the present value of $200,000 to be received at the end of each of four years, using an interest rate of 7%, compounded annually, as follows: a. By successive computations, using the present value of $1 table in Exhibit 5. Round to the nearest whole dollar. First year $ Second Year Third Year Fourth Year Total present value $ b. By using the present value of an annuity of $1 table in Exhibit 7. Round to the nearest whole dollar. $ c. Why is the present value of the four $200,000 cash receipts less than the $800,000 to be received in the future? The present value is less due to the compounding of interest over the 4 years.

Explanation / Answer

PVIF = 1 / (1+i)^N
PVIF(1, 7%) = 1 / (1+7%)
= 1 / (1+ 0.07)
= 1 / 1.07
= 0.9346

PVIF(2, 7%) = 1 / (1+7%)^2
= 1 / (1.07)^2
= 1 / 1.1449
= 0.8734

PVIF(3, 7%) = 1 / (1+7%)^3
= 1 / (1.07)^3
= 1 / 1.225043
= 0.8163

PVIF(4, 7%) = 1 / (1+7%)^4
= 1 / (1.07)^4
= 1 / 1.31079601
= 0.7629

And the present value of annuity would be calculated as

200,000 * 0.9346 +
200,000 * 0.8734 +
200,000 * 0.8163 +
200,000 * 0.7629 = $ 677,440

Value of four $ 200000 is less than $ 800000 because what we are doing here is calculating present values which is the discounted value.

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