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.)
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.