College is expected to cost $150,000 per year in 18 years, how much should you begin depositing annually at the end of each year to accumulate enough funds to pay the first years tuition at the beginning of the 19th year? earning 6% annual rate of return of the investment
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
For tax purposes, business frequently depreciate equipment.
To calculate how much you should begin depositing annually at the end of each year, we need to use the future value of an ordinary annuity formula. The formula for the future value of an ordinary annuity is:
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.