A grandparent puts $5,000 into a college education fund for a grandchild. If the fund earns 3.75% annual interest compounded daily, what is the value (in dollars) of the account after 18 years? Assume all years have 365 days. (Round your answer to the nearest cent.)

Answer 1

To calculate the value of the account after 18 years with compound interest, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (initial deposit)
r = annual interest rate (as a decimal)
n = number of times that interest is compounded per year
t = number of years the money is invested/borrowed for

In this case:
P = $5,000
r = 3.75% = 0.0375
n = 365 (compounded daily)
t = 18 years

Plugging these values into the formula:

A = $5,000(1 + 0.0375/365)^(365*18)
A = $5,000(1 + 0.0001027)^(6570)
A = $5,000(1.0001027)^(6570)
A = $5,000(1.836209)

A = $9,181.05

Therefore, the value of the account after 18 years would be approximately $9,181.05.