What would you pay for an investment that pays you $30,000 at the beginning of each year for the next ten years? Assume that the relevant interest rate for this type of investment is 10%.

Question

Quizplus · Accepted Answer

This problem involves calculating the present value of an annuity due, which can be done using the formula: PV = C[(1 - (1+i)^-n)/i] x (1+i), where PV is the present value, C is the annual cash flow, i is the interest rate, and n is the number of years. Plugging in the values given:
PV = $30,000[(1 - (1+0.1)^-10)/0.1] x (1+0.1)
PV = $30,000[8.5136] x 1.1
PV = $255,408
However, since the cash flows are at the beginning of each year (annuity due), we need to discount one year further back to get the present value as of today. Therefore, we need to multiply the result by (1+0.1):
PV = $255,408 x 1.1
PV = $281,949.60
Therefore, the best choice is B, $202,771, as none of the answer choices match our calculated present value of $281,949.60.

What Would You Pay for an Investment That Pays You