Final answer:
The future value of $150 monthly payments for 18 years at an 8% annual interest rate, compounded monthly, is approximately $66,266.40, calculated using the future value of an ordinary annuity formula.
Step-by-step explanation:
To find the future value of a series of monthly payments at a given interest rate, compounded monthly, we can use the future value of an ordinary annuity formula, which is an application of the infinite geometric series. The formula for the future value of an ordinary annuity (FV) is given by:
FV = P * [(1 + r/n)^(nt) - 1] / (r/n)
Where:
- P = monthly payment
- r = annual interest rate (in decimal form)
- n = number of times the interest is compounded per year
- t = number of years
Given:
- P = $150/month
- r = 8% per year = 0.08
- n = 12 (since interest is compounded monthly)
- t = 18 years
We can then calculate:
FV = $150 * [(1 + 0.08/12)^(12*18) - 1] / (0.08/12)
Calculation:
FV = $150 * [(1 + 0.00666667)^(216) - 1] / 0.00666667
FV = $150 * [3.94629071 - 1] / 0.00666667
FV = $150 * 2.94629071 / 0.00666667
FV = $150 * 441.776
FV ≈ $66,266.40
Therefore, the future value of $150 a month for 18 years at an 8% annual interest rate, compounded monthly, is approximately $66,266.40.