Answer-
He needs to put $10345 in the account today, in order to get 15000 in five years.
Solution-
We know that,
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
Where,
A = future value of the investment with interest = 15000
P = principal investment amount
r = annual interest rate (decimal) = 7.5% = 0.075
n = number of times that interest is compounded per year = 4
t = the number of years the money is invested = 5
Putting the values,
[tex]15000=P(1+\frac{0.075}{4})^{4 \times 5}[/tex]
[tex]\Rightarrow P=\frac{15000}{(1+0.01875)^{20}} =\frac{15000}{1.01875^{20}} =\frac{15000}{1.45} =10344.8 \approx 10345[/tex]
