Question

b. Brenda Young desires to have $9,000 eight years from now for her daughter’s college fund. If she will earn 7 percent (compounded annually) on her money, what amount should she deposit now? Use the present value of a single amount calculation. (Round PV factor to 3 decimal places and final answer to the nearest whole dollar.)

Answer 1

Answer:

$5239

Explanation:

We will use future value formula to solve our given problem.

$FV=PV(1+\frac{r}{n})^{nT}$, where,

$FV=\text{Future value}$,

$PV=\text{Present value}$,

$r=Annual interest rate in decimal form$,

$n=\text{Number of periods interest is compounded}$,

$T=\text{Time in years}$.

$7\%=\frac{7}{100}=0.07$

$\ 9,000=PV(1+\frac{0.07}{1})^{1*8}$

$\ 9,000=PV(1+0.07)^{8}$

$\ 9,000=PV(1.07)^{8}$

$PV(1.07)^{8}=\ 9,000$

$PV*1.7181861798=\ 9,000$

Rounding PV factor to 3 decimal places:

$PV*1.718=\ 9,000$

$\frac{PV*1.718}{1.718}=\frac{\ 9,000}{1.718}$

$PV=\ 5238.649592549476135$

$PV\approx \ 5239$

Therefore, Brenda should deposit $5239 now.