Find the future value of an annuity with payments of $800 per month for 5 years if the interest
rate is 6% compounded monthly, and find the total interest earned.
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The future value of an annuity can be calculated using the formula:
FV = P * [(1 + r/n)^(nt) - 1] / (r/n)
where:
FV = future value
P = payment amount per period
r = annual interest rate (in decimal form)
n = number of compounding periods per year
t = number of years
In this case, P = $800, r = 6% or 0.06, n = 12 (since it's compounded monthly), and t = 5.
So, the future value of the annuity is:
FV = 800 * [(1 + 0.06/12)^(12*5) - 1] / (0.06/12)
FV = 800 * [(1 + 0.005)^(60) - 1] / 0.005
FV = 800 * [1.34856 - 1] / 0.005
FV = 800 * 0.34856 / 0.005
FV = $55,769.60
The total interest earned is the future value minus the total amount of payments made. The total amount of payments made is $800 per month for 5 years, or $800 * 12 * 5 = $48,000.
So, the total interest earned is $55,769.60 - $48,000 = $7,769.60.
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