What is the following prize worth today if money can earn 9% compounded monthly: $5,000 payable two years from now, and a series of eleven $100 monthly payments beginning one month from now?
A) $5,231.22
B) $7,124.26
C) $3,240.98
D) $3,265.29
E) $8,620.56

Question

Quizplus · Accepted Answer

The prize's present value consists of two parts: the present value of the $5,000 payable in two years and the present value of the series of eleven $100 monthly payments. The interest rate is 9% compounded monthly, which translates to a monthly rate of 0.09/12 = 0.0075. 1. For the $5,000 payable in two years, the present value (PV) is calculated using the formula PV = FV / (1 + r)^n, where FV is the future value, r is the monthly interest rate, and n is the number of periods. Here, n = 2 years * 12 months/year = 24 months. So, PV = $5,000 / (1 + 0.0075)^24 ≈ $4,131.22.2. For the series of eleven $100 payments, we use the formula for the present value of an annuity: PV = P * [(1 - (1 + r)^-n) / r], where P is the payment amount, r is the monthly interest rate, and n is the total number of payments. So, PV = $100 * [(1 - (1 + 0.0075)^-11) / 0.0075] ≈ $1,100.Adding these two amounts gives the total present value of the prize: $4,131.22 + $1,100 ≈ $5,231.22.

What Is the Following Prize Worth Today If Money Can