Answer to Question #143302 in Financial Math for Gilbert

Question

A company will need $75,000 in 5 years. To meet this goal the company deposits money in an account today that pays 11% annual interest compounded quarterly. What amount should be invested to total $75,000 in 5 years?

Answer 1

$\bold {Answer}$

Amount to be invested today to total $\$75, 000$ in 5 years:

$PV = \$43,593.79$

$\bold {Solution}$

We are provided:

Future value, $FV = \$75,000$

Annual interest rate, $i\% = \$11\%$

Number of compounding periods, $m = 4$

Number of years, $n = 5 \space years$

Required:

Present value, $PV = ?$

The formular for future value is given by: $FV = PV \left (1 + \dfrac {i}{m}\right)^{mn}$

$=> \$75,000 = PV \left (1 + \dfrac {0.11}{4}\right)^{(4×5)}$

$=> \$75,000 = PV \left (1 + 0.0275 \right)^{20}$

$=> \$75,000 = PV \left (1.0275 \right)^{20}$

$=> PV =\dfrac { \$75,000}{1.0275^{20}}$

$= \dfrac {\$75,000}{1.7204284313}$

$= \$43,593.792474$

$=\bold {\$43,593.79}$