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FinanceFundamentals of Financial Management (MindTap Course List)FUTURE VALUE OF AN ANNUITY Kind the future values of the following ordinary annuities: a. FV of $400 paid each 6 months for 5 years at a nominal rate of 12% compounded semiannually b. FV of $200 paid each 3 months for 5 years at a nominal rate of 12% compounded quarterly c. These annuities receive the same amount of cash during the 5-year period and earn interest at the same nominal rate, yet the annuity in part b ends up larger than the one in part a. Why does this occur?BuyFind*arrow_forward*

15th Edition

Eugene F. Brigham + 1 other

Publisher: Cengage Learning

ISBN: 9781337395250

Chapter 5, Problem 25P

Textbook Problem

**FUTURE VALUE OF AN ANNUITY** Kind the future values of the following ordinary annuities:

- a. FV of $400 paid each 6 months for 5 years at a nominal rate of 12% compounded semiannually
- b. FV of $200 paid each 3 months for 5 years at a nominal rate of 12% compounded quarterly
- c. These annuities receive the same amount of cash during the 5-year period and earn interest at the same nominal rate, yet the annuity in part b ends up larger than the one in part a. Why does this occur?

Expert Solution

**a.**

Summary Introduction

**To compute:** Future value of annuity of $400 paid each 6 months for 5 years at a nominal rate of 12% compounded semiannually.

**Future value of annuity:** It states the value of regular payments that are made at a future date. The future value is defined by the specified rate of return or by the discount rate. If there is a fluctuation in regular payments then each of the cash flow is to be computed to get the future value of annuity.

Formula to calculate future value of annuity is,

Where,

- FV is future value of annuity.
- PMT is periodic monthly payment.
- I is interest rate.
- N is number of periods.

Substitute $400 for PMT 12% for I and 5 years for N and 2 for T.

Expert Solution

**b.**

Summary Introduction

**To compute:** Future value of annuity of $200 paid each 3 months for 5 years at a nominal rate of 12% compounded quarterly.

**Future value of annuity:** It states the value of regular payments that are made at a future date. The future value is defined by the specified rate of return or by the discount rate. If there is a fluctuation in regular payments then each of the cash flow is to be computed to get the future value of annuity.

Expert Solution

**c.**

Summary Introduction

**To explain:** The reason for annuity in part (b) is larger than annuity in part (a).

**Future value of annuity:** It states the value of regular payments that are made at a future date. The future value is defined by the specified rate of return or by the discount rate. If there is a fluctuation in regular payments then each of the cash flow is to be computed to get the future value of annuity.

Fundamentals of Financial Management (MindTap Course List)

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