Suppose you are going to receive $9,500 per year for five years. The appropriate interest rate is...

Question:

Suppose you are going to receive $9,500 per year for five years. The appropriate interest rate is 11%.

Requirement 1:

a) What is the present value of the payments if they are in the form of an ordinary annuity? (Enter rounded answer as directed, but do not use rounded numbers in intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

b) What is the present value of the payments if the payments are an annuity due? (Enter rounded answer as directed, but do not use rounded numbers in intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

Requirement 2:

a) Suppose you plan to invest the payments for five years. What is the future value if the payments are an ordinary annuity? (Enter rounded answer as directed, but do not use rounded numbers in intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

b) What is the future value if the payments are an annuity due? (Enter rounded answer as directed, but do not use rounded numbers in intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

Ordinary Annuity and Annuity Due:

An ordinary annuity has payments occurring at the end of each period. In contrast, an annuity due has payments occurring at the beginning of each period. All else the same, the present value of an annuity due is higher than that of an ordinary annuity.

Answer and Explanation:

1a) We can use the following formula to compute the present value of an annuity with periodic payment {eq}M {/eq} for {eq}T{/eq} periods, given periodic return {eq}r{/eq}:

  • {eq}\displaystyle \frac{M(1 - (1 + r)^{-T})}{r} {/eq}

Applying the formula, the present value of the annuity is:

  • {eq}\displaystyle \frac{9,500(1 - (1 + 11\%)^{-5})}{11\%} = 35,111.02 {/eq}

1b) The present value of an annuity due is calculated as follows:

  • present value of annuity due = present value of annuity *(1 + interest rate)
  • present value of annuity due = 35,111.02 *(1 + 11%)
  • present value of annuity due = 38,973.23

2a) We can use the following formula to compute the future value of an annuity with periodic payment {eq}M {/eq} for {eq}T{/eq} periods, given periodic return {eq}r{/eq}:

  • {eq}\displaystyle \frac{M((1 + r)^T - 1)}{r} {/eq}

Applying the formula, the future value of the annuity is:

  • {eq}\displaystyle \frac{9,500((1 + 11\%)^5 - 1)}{11\%} = 59,164.11 {/eq}

2b) The future value of an annuity due is calculated as follows:

  • future value of annuity due = future value of annuity *(1 + interest rate)
  • future value of annuity due = 59,164.11 *(1 + 11%)
  • future value of annuity due = 65,672.16

Learn more about this topic:

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How to Calculate the Present Value of an Annuity

from Business 110: Business Math

Chapter 8 / Lesson 3
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