Question

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.

Short answer

Answer

The future value of the annuity is $67,103.49.

Step-by-step solution

Identification of the required information

Payment (PMT) = $1,800

Periods for annual compounding (n) = 15

Interest Rate for annual compounding (i) = 12%

Future value of annuity (FA)

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