Final answer:
To calculate the interest earned from a quarterly-contributing annuity with a 5% annual interest rate over 20 years, use the future value annuity formula and subtract the total contributions from the obtained future value to find the interest.
Step-by-step explanation:
To calculate the total amount of interest earned from an annuity with quarterly contributions at a 5% annual interest rate, compounded quarterly, over 20 years, we must first calculate the future value of the annuity. For an annuity with regular contributions, the future value is calculated using the formula for the future value of an annuity due:
FV = P * [((1 + r/n)^(nt) - 1) / (r/n)]
where FV is the future value of the annuity, P is the quarterly payment, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.
Given:
- P = $400
- r = 0.05 (5%)
- n = 4 (quarterly)
- t = 20
We can now calculate the FV:
FV = 400 * [((1 + 0.05/4)^(4*20) - 1) / (0.05/4)]
Calculating this gives us the total value of the annuity after 20 years. To find the interest earned, we subtract the total contributions from the future value:
Interest Earned = FV - (P * n * t)
In this case, the total contributions are 400 * 4 * 20, which equals $32,000. After finding FV using the formula above, we can calculate the interest earned directly:
This process will give the direct answer to the amount of interest accumulated over the 20-year period in the annuity investment.