Explanation:
The formula to calculate the future value of a present value deposit with compounding interest is:
FV = PV × (1 + r/n)^(n*t)
Where:
PV = Present Value (the initial deposit)
r = Annual interest rate (as a decimal)
n = Number of compounding periods per year
t = Number of years
Using this formula, we can calculate the future value of the $6000 deposit after 15 years:
PV = $6000
r = 6% = 0.06
n = 4 (compounded quarterly, i.e. 4 times per year)
t = 15 years
FV = $6000 × (1 + 0.06/4)^(4*15)
FV = $6000 × 1.458^60
FV = $6000 × 6.2565
FV = $37,539.00
Therefore, the future value of the $6000 deposit after 15 years with quarterly compounding at 6% interest rate is $37,539.00.