What is the present value of monthly payments of $1000 for 5 years followed by monthly payments of $500 for 10 years (first payment one month from now)if j₁₂ = 4.8%? A)$89,485.08 B)$90,692.96 C)$100,826.85 D)$115,238.16

Question

Quizplus · Accepted Answer

We can use the formula for present value of an annuity to solve this problem. We will have two annuities, one with a payment of $1000 for 5 years and one with a payment of $500 for 10 years.

Present value of first annuity: 
PV1 = A * [(1 - (1 + r)^-n) / r] 
PV1 = 1000 * [(1 - (1 + 0.048/12)^-(5*12)) / (0.048/12)] 
PV1 = $54,582.95

Present value of second annuity: 
PV2 = A * [(1 - (1 + r)^-n) / r] 
PV2 = 500 * [(1 - (1 + 0.048/12)^-(10*12)) / (0.048/12)] 
PV2 = $36,110.01

Total present value: 
PV = PV1 + PV2 
PV = $90,692.96

Therefore, the best choice is B.

What Is the Present Value of Monthly Payments of $1000