You want to have a $ 74,468 college fund in 13 years. How much will you have to deposit now in an account with an APR of 3 % and monthly compounding?
74468 = a * [1 + (.03 / 12)]^(12 * 13)
log(74468) = log(a) + 156 log(1.0025)
or
a = 74468/(1.0025)^156
= $50,443.62
To calculate the amount you will need to deposit now in order to have a specific amount in the future, we can use the formula for compound interest:
A = P (1 + r/n)^(nt)
Where:
A = the future amount
P = the principal amount (initial deposit)
r = annual interest rate (expressed as a decimal)
n = number of times the interest is compounded per year
t = number of years
In this case, you want to calculate P, the initial deposit. We know the future amount (A), the annual interest rate (r), the number of compounding periods per year (n), and the number of years (t).
First, let's convert the annual interest rate to a decimal: 3% = 0.03.
Since compounding is done monthly, we have 12 compounding periods per year, so n = 12.
Now, let's plug in the values into the formula:
A = $74,468
r = 0.03
n = 12
t = 13
$74,468 = P (1 + 0.03/12)^(12*13)
To solve for P, we can rearrange the equation:
P = $74,468 / (1 + 0.03/12)^(12*13)
P ≈ $41,999.76
Therefore, you will need to deposit approximately $41,999.76 now in an account with an APR of 3% and monthly compounding to have a college fund of $74,468 in 13 years.