Present value of annuities Your uncle has said that if you agree to finish colle

Question

Present value of annuities Your uncle has said that if you agree to finish college he will give you equal payments of $2,000 at the end of each year for the next seven years. If the annual interest rate stays constant at 7%, what is the value of these payments in today's dollars? Round your answer to the nearest whole dollar. $9,162 $11,534 $10,779 $13,474 You found out that now you are going to receive payments of $5,500 for the next 16 years. You will receive these payments at the beginning of each year. The annual interest rate will remain constant at 14%. What is the present value of these payments? Round your answer to the nearest whole dollar. $34,458 $53,031 $39,282 $31,426

Explanation / Answer

Solution:

1) Calculation of Annuity Present Value:

Annuity Present Value (PVA) = C ({1-[1/ (1+r)] t}/ r)

= 2,000 ({1-[1/ (1+0.07)] 7}/ 0.07)

= 2,000 ({1-[0.934579] 7}/ 0.07)

= 2,000 ({1-0.62275}/ 0.07)

= 2,000 (0.37725/ 0.07)

= 2,000 * 5.3892857

= 10,779

2) Calculation of Annuity Present Value:

Annuity Present Value (PVA) = C ({1-[1/ (1+r)] t}/ r)

= 5,500 ({1-[1/ (1+0.14)] 16}/ 0.14)

= 5,500 ({1-0.12288}/ 0.14)

= 5,500 (0.87712/ 0.14)

= 5,500 * 6.265143

= 34,458

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