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.

Answer 1

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.