A couple deposits $16,000 into an account earning 6% annual interest for 25 years. Calculate the future value of the investment if the interest is compounded daily. Round your answer to the nearest cent.
To calculate the future value of the investment with daily compounding, we can use the formula:
FV = P(1 + r/n)^(nt)
Where:
FV = Future Value
P = Principal amount (initial deposit)
r = annual interest rate (in decimal form)
n = number of times the interest is compounded per year
t = number of years
In this case:
P = $16,000
r = 6% or 0.06
n = 365 (daily compounding)
t = 25 years
Now plug the values into the formula:
FV = $16,000(1 + 0.06/365)^(365*25)
FV = $16,000(1 + 0.000164383)^(9125)
FV = $16,000(1.000164383)^(9125)
FV = $16,000(2.26749071)
FV = $36,479.86
Therefore, the future value of the investment after 25 years with daily compounding is $36,479.86.