Joseph desires to purchase an annuity on January 1, 2010, that yields him five annual rents of $10, 000 each, with the first rent to be received on January 1, 2013.The interest rate is 10% compounded annually.The cost (present value)of the annuity on January 1, 2010, is
A)$31, 328.81
B)$34, 461.70
C)$37, 907.87
D)$48, 684.19

Question

Quizplus · Accepted Answer

The cost of the annuity on January 1, 2010, can be calculated using the present value formula for an annuity. Since the first payment is received on January 1, 2013, we need to discount the annuity that starts in 2013 back to January 1, 2010. The formula for the present value of an annuity is PV = P * [(1 - (1 + r)^-n) / r], where P is the payment amount, r is the interest rate per period, and n is the number of periods. However, because the first payment is not immediate, we need to adjust for the delay by discounting the result back two years (from 2013 to 2010). The calculation is as follows:PV = $10,000 * [(1 - (1 + 0.10)^-5) / 0.10] = $10,000 * 3.790787Then, discount this result back two years (to account for the start in 2013): PV_2010 = PV_2013 / (1 + 0.10)^2PV_2010 = $37,907.87 / (1.21) = $31,328.81Therefore, the correct answer is $31,328.81.

Joseph Desires to Purchase an Annuity on January 1, 2010