John Regan, an employee at Home Depot, made deposits of $870 at the end of each year for 5 years. Interest is 5% compounded annually. What is the value of Regan’s annuity at the end of 5 years?
Question
John Regan, an employee at Home Depot, made deposits of $870 at the end of each year for 5 years. Interest is 5% compounded annually. What is the value of Regan’s annuity at the end of 5 years?
Solution
To calculate the value of John Regan's annuity at the end of 5 years, we can use the formula for the future value of an ordinary annuity. The formula is:
FV = P * [(1 + r)^nt - 1] / r
where: FV = future value of the annuity P = amount deposited each year r = interest rate n = number of times interest is compounded per year t = number of years
In this case: P = $870 r = 5% or 0.05 n = 1 (since interest is compounded annually) t = 5 years
Substituting these values into the formula, we get:
FV = 870 * [(1 + 0.05)^5 - 1] / 0.05
First, calculate the value inside the brackets:
(1 + 0.05)^5 - 1 = 1.2762815625 - 1 = 0.2762815625
Then, multiply this by 870 and divide by 0.05:
FV = 870 * 0.2762815625 / 0.05 = $4843.54
So, the value of Regan's annuity at the end of 5 years is approximately $4843.54.
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