150,000 = A*[1.06)^18 -1]/0.06
Where A is the required annual contribution, made n = 18 times.
150,000 = A*30.906
A = $4853.48
Where A is the required annual contribution, made n = 18 times.
150,000 = A*30.906
A = $4853.48
FV = P * [(1 + r)^n - 1] / r
Where:
FV = Future value (the amount you want to accumulate)
P = Annual deposit
r = Annual interest rate (expressed as a decimal)
n = Number of periods
In this case, the future value (FV) is $150,000, the annual interest rate (r) is 6% (or 0.06 as a decimal), and the number of periods (n) is 18 (since you want to accumulate enough funds in 18 years).
We can rearrange the formula to solve for the annual deposit (P):
P = FV * (r / [(1 + r)^n - 1])
Substituting the given values into the formula:
P = $150,000 * (0.06 / [(1 + 0.06)^18 - 1])
Now we can calculate it:
P = $150,000 * (0.06 / [1.06^18 - 1])
Using a calculator:
P = $150,000 * 0.06 / 9.43945058
P ≈ $961.54
So, you should begin depositing approximately $961.54 annually at the end of each year to accumulate enough funds to pay the first year's tuition at the beginning of the 19th year, assuming a 6% annual rate of return on the investment.