Kelly starting setting aside funds six years ago to buy some new equipment for her firm. She has saved $2,000 each quarter and earned a return of 7.50% p.a. compounded quarterly. How much money does she currently have saved for this purpose? Group of answer choices $61,803.48 $61,666.67 $62,224.04 $59,924.38 $59,022.03
Question
Kelly starting setting aside funds six years ago to buy some new equipment for her firm. She has saved $2,000 each quarter and earned a return of 7.50% p.a. compounded quarterly. How much money does she currently have saved for this purpose?
Group of answer choices
$61,803.48
$61,666.67
$62,224.04
$59,924.38
$59,022.03
Solution
To calculate the amount of money Kelly currently has saved, we can use the formula for the future value of a series of regular payments compounded quarterly:
FV = P * [(1 + r)^n - 1] / r
where:
- FV is the future value
- P is the regular payment per period ($2,000)
- r is the interest rate per period (7.50% or 0.075 divided by 4)
- n is the number of periods (6 years multiplied by 4 quarters per year)
Substituting the given values into the formula, we get:
FV = $2,000 * [(1 + 0.075/4)^(6*4) - 1] / (0.075/4)
Calculating this expression, we find that Kelly currently has saved approximately 61,803.48.
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