Jack and Jill are saving for a rainy day and decide to put $50 away in their local bank every year for the next twenty-five years. The local Up-the-Hill Bank will pay them 7% on their account. If Jack and Jill put the money in the account faithfully at the end of every year, how much will they have in it at the end of twenty-five years? Round your answer to the nearest dollar. (NOTE, do NOT include the dollar sign in your answer.)
Question
Jack and Jill are saving for a rainy day and decide to put $50 away in their local bank every year for the next twenty-five years. The local Up-the-Hill Bank will pay them 7% on their account. If Jack and Jill put the money in the account faithfully at the end of every year, how much will they have in it at the end of twenty-five years? Round your answer to the nearest dollar. (NOTE, do NOT include the dollar sign in your answer.)
Solution
This is a problem of future value of a series of payments, or an annuity. The formula for the future value of an annuity is:
FV = P * [(1 + r)^n - 1] / r
where: FV = future value P = payment per period r = interest rate per period n = number of periods
In this case: P = $50 r = 7% or 0.07 n = 25 years
Substituting these values into the formula gives:
FV = $50 * [(1 + 0.07)^25 - 1] / 0.07
Calculating the expression in the brackets first:
(1 + 0.07)^25 - 1 = 13.7652
Then multiply by $50 and divide by 0.07:
FV = 9825.14
Rounding to the nearest dollar gives $9825.
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