To achieve exactly a 13% rate of return, how much would need to be invested today in an investment that returns $12,000 at the end of 3 years and $10,000 at the end of 5 years? Round to the nearest whole number.

Question

Quizplus · Accepted Answer

To find the present value (PV) of future cash flows at a 13% rate of return, we use the formula for the present value of a single sum, which is PV = FV / (1 + r)^n, where FV is the future value, r is the rate (expressed as a decimal), and n is the number of periods. For the $12,000 due in 3 years: PV = $12,000 / (1 + 0.13)^3 = $12,000 / 1.4394 = $8,335.93. For the $10,000 due in 5 years: PV = $10,000 / (1 + 0.13)^5 = $10,000 / 1.8481 = $5,409.52. Adding these together gives the total amount needed to be invested today: $8,335.93 + $5,409.52 = $13,745.45, which rounds to $13,745.

To Achieve Exactly a 13% Rate of Return, How Much