You want to have $60,000 college fund in 12 years. How much will you have to deposit now under the scenario below. Assume that you make no deposits into the account after the initial deposit.
An APR of 8% compounded daily. I know how to break the problem down, but I am not understanding how to get the answer.
To calculate the amount you need to deposit now to have a $60,000 college fund in 12 years, under the given scenario of an Annual Percentage Rate (APR) of 8% compounded daily, you can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment ($60,000 in this case)
P = the principal amount (the amount you need to deposit now)
r = the annual interest rate (8% in this case, written as a decimal, so 0.08)
n = the number of times the interest is compounded per year (365 times, as it is compounded daily)
t = the number of years (12 years in this case)
Now, substitute the known values into the formula:
60,000 = P(1 + 0.08/365)^(365*12)
Simplify the formula:
60,000 = P(1 + 0.000219178)^4380
Now, solve for P. To do that, divide both sides of the equation by (1 + 0.000219178)^4380:
P = 60,000 / (1 + 0.000219178)^4380
Using a calculator to perform the calculations, the result is approximately $24,560.36.
Therefore, you would need to deposit approximately $24,560.36 now to have a $60,000 college fund in 12 years, with an APR of 8% compounded daily.
P2 = P1(1+r)^n = $60,000.
r = 0.08/365 = 0.00021918/day = Daily % rate expressed as a decimal.
n = 365Comp/yr. 12yrs. = 4380 Compounding periods.
P1(1.00021918)^4380 = 60,000.
P1 = ?.