Annuities
The future value (FV) of an annuity is given by:
[tex]FV=A\cdot\frac{(1+i)^n-1}{i}[/tex]Where:
A is the value of the annuity or the regular payment
i is the interest rate adjusted to the compounding period
n is the number of periods of the investment (or payment)
The given values are:
A = $38,000
n = 7 years
i = 8% = 0.08
Substituting:
[tex]\begin{gathered} FV=\$38,000\cdot\frac{(1+0.08)^7-1}{0.08} \\ FV=\$38,000\cdot\frac{(1.08)^7-1}{0.08} \\ \text{Calculate:} \\ FV=\$38,000\cdot\frac{0.7138243}{0.08} \\ FV=\$38,000\cdot8.9228 \\ FV=\$339,066.53 \end{gathered}[/tex]The future value is $339,066.53
