Dana invests $8,000 into her son college fund when he is born. The college fund earns 3% interest and is compounded daily. What will the value of his account be if he takes the money out at 18 to go to college? Please write answer rounding to 2 decimal places.
8000(1+.03/365)^(365*18) = ?
To calculate the value of Dana's son's college fund when he takes the money out at the age of 18, we need to use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal amount (initial investment)
r = annual interest rate (expressed as a decimal)
n = number of times interest is compounded per year
t = number of years
In this case, Dana invests $8,000, the interest rate is 3% (or 0.03 as a decimal), the interest is compounded daily, and the investment period is 18 years.
First, let's convert the interest rate to a daily rate:
daily interest rate = (1 + r)^(1/n) - 1 = (1 + 0.03)^(1/365) - 1
Next, we can calculate the future value of the investment:
A = 8,000 * (1 + daily interest rate)^(365 * 18)
Finally, let's calculate the answer:
A = 8,000 * (1 + ((1 + 0.03)^(1/365) - 1))^(365 * 18)
Using a calculator or spreadsheet software, we find that the value of Dana's son's college fund, when he takes the money out at 18 years old, would be approximately $13,334.15 (rounded to 2 decimal places).