A professional soccer player has a deferred compensation annuity that pays her $2,900 at the end of each month for 8 years. If the annual interest rate is 5% compounded monthly, find the present value of the annuity. (Round your answer to the nearest cent.)
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To find the present value of the annuity, we can use the formula for the present value of an annuity due:
PV = PMT * [(1 - (1 + r)^-n) / r]
where PV is the present value, PMT is the monthly payment, r is the monthly interest rate, and n is the total number of payments.
In this case, PMT = $2,900, r = 5%/12 = 0.05/12 = 0.00417, and n = 8 years * 12 months/year = 96 months.
Plugging these values into the formula, we get:
PV = $2,900 * [(1 - (1 + 0.00417)^-96) / 0.00417]
PV = $2,900 * [(1 - (1.00417)^-96) / 0.00417]
PV = $2,900 * [(1 - 0.341316) / 0.00417]
PV = $2,900 * (0.658684 / 0.00417)
PV = $2,900 * 157.925
PV = $457,345.50
Therefore, the present value of the annuity is approximately $457,345.50.
no
I apologize for the mistake in my calculation. Let me correct it.
The correct formula to use in this case is the formula for the present value of an ordinary annuity:
PV = PMT * [(1 - (1 + r)^-n) / r]
where PV is the present value, PMT is the monthly payment, r is the monthly interest rate, and n is the total number of payments.
Plugging in the values, we have:
PMT = $2,900
r = 5%/12 = 0.05/12 = 0.00417
n = 8 years * 12 months/year = 96 months
PV = $2,900 * [(1 - (1 + 0.00417)^-96) / 0.00417]
PV = $2,900 * [(1 - (1.00417)^-96) / 0.00417]
PV = $2,900 * [(1 - 0.3432) / 0.00417]
PV = $2,900 * (0.6568 / 0.00417)
PV = $2,900 * 157.5171
PV = $456,581.99
Therefore, the correct present value of the annuity is approximately $456,581.99.