Your goal is to create a college fund for your child. Suppose you find a fund that offers an APR of 5%. How much should you deposit monthly to accumulate $83,000 in 18 years?
The divisor should have been .05/12 , not .05
Just use your formula to solve for P
P((1+.05/12)^(12*18) - 1)/.05 = 83000
To calculate the monthly deposit needed to accumulate a specific amount of money in a given time frame, we can use the formula for the future value of an ordinary annuity. The formula is:
FV = (PMT × ((1 + r)^n - 1)) / r
Where:
FV = Future value
PMT = Monthly deposit amount
r = Monthly interest rate
n = Number of months
Given:
FV = $83,000
r = 5% APR = 5% / 12 = 0.4167% monthly interest rate
n = 18 years × 12 months/year = 216 months
Substituting these values into the formula, we can solve for PMT:
$83,000 = (PMT × ((1 + 0.004167)^216 - 1)) / 0.004167
To solve for PMT, we can rearrange the formula:
PMT = (FV × r) / ((1 + r)^n - 1)
PMT = ($83,000 × 0.004167) / ((1 + 0.004167)^216 - 1)
Calculating this using a calculator or spreadsheet, we find that the monthly deposit needed to accumulate $83,000 in 18 years with a 5% APR is approximately $210.22.