   Chapter 5, Problem 6P Fundamentals of Financial Manageme...

15th Edition
Eugene F. Brigham + 1 other
ISBN: 9781337395250

Solutions

Chapter
Section Fundamentals of Financial Manageme...

15th Edition
Eugene F. Brigham + 1 other
ISBN: 9781337395250
Textbook Problem

FUTURE VALUE: ANNUITY VERSUS ANNUITY DUE What’s the future value of a 5%, 5-year ordinary annuity that pays $800 each year? If this was an annuity due, what would its future value be? Summary Introduction To determine: The future value of the annuity and the future value of an annuity due. Introduction: Annuity: An annuity refers to the fixed cash flows that are received or paid by a person at defined intervals. This series of cash flows occur for a given time period. The two kinds of annuities are the annuities having a fixed rate and annuities having a variable rate. The payment of annuities is made at the end of the year. Annuity Due: The annuity due refers to the fixed cash flows that are received or paid by a person at defined intervals. It is same as annuity but the annuity due is paid at the beginning of the year. Explanation Given, The monthly payment is$800.

The rate of interest is 5% or 0.05.

The time period is 5 years.

Future value of an ordinary annuity

The formula to calculate the future value of the annuity is:

FVAnnuity=C×((1+I)N1I)

Where,

• FV is the future value.
• C is the monthly payment.
• I is the interest rate.
• N is the time period.

Substitute $800 for C, 5 for N, and 0.05 for I in the above formula. FVAnnuity=$800×((1+0.05)510.05)=$800×((1.05)510.05)=$800×5.525631=\$4,420

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