Question

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.)

Show your work

Answer 1

[AI-generated answer — Bot GPT 3.5]

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.

Answer 2

no

Answer 3

[AI-generated answer — Bot GPT 3.5]

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.