91Ó°ÊÓ

Question: As stated in the chapter, annuity payments are assumed to come at the end of each payment period (termed an ordinary annuity). However, an exception occurs when the annuity payments come at the beginning of each period (termed an annuity due). To find the present value of an annuity due, the annuity formula must be adjusted as to the following: PVAD 5 A 3 ( 12 1 ________ (11i) n 21 ___________ i 11) The Capital Budgeting Process blo7716x_ch09_255-294.indd 284. Likewise, the formula for the future value of an annuity due requires a modification: FVAD 5 A 3 ( (11i) n11 21 ___________ i 21). What is the future value of a 15-year annuity of $1,800 per period where payments come at the beginning of each period? The interest rate is 12 percent.

Step by step solution

01

Identification of the required information

Payment (PMT) = $1,800

Periods for annual compounding (n) = 15

Interest Rate for annual compounding (i) = 12%

02

Future value of annuity (FA)

$$\begin{gathered} \mathit{F}\mathit{A}\mathbf{=}\mathit{P}\mathit{M}\mathit{T}\mathbf{×}\left[\frac{{(1+i)}^{n+1}-1}{i}\right] \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{18}\mathbf{,}\mathbf{00}\mathbf{×}\mathbf{\left[}\frac{{\mathbf{(}\mathbf{1}\mathbf{+}\mathbf{12}\mathbf{\%}\mathbf{)}}^{\mathbf{15}\mathbf{+}\mathbf{1}}\mathbf{-}\mathbf{1}}{\mathbf{12}\mathbf{\%}}\mathbf{\right]} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{75}\mathbf{,}\mathbf{155}\mathbf{.}\mathbf{90} \end{gathered}$$

Unlock Step-by-Step Solutions & Ace Your Exams!

• Full Textbook Solutions

  Get detailed explanations and key concepts

• Unlimited Al creation

  Al flashcards, explanations, exams and more...

• Ads-free access

  To over 500 millions flashcards

• Money-back guarantee

  We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!