Assume your uncle will pay you $100 for each of the next two years and $200 in years 3 and these amounts will be paid at year end. Assume the interest rate is 10% for the first two years and 12% for the next two (years 3 and 4). What is your uncle's promise worth in today's dollars? (Round your answer)
A) $317
B) $342
C) $453
D) $512
E) $600

Question

Quizplus · Accepted Answer

To calculate the present value of the payments, we need to discount them to today's dollars using the given interest rates.

For the first two years, we can use the present value of an annuity formula:

PV = C * [(1 - (1+r)^-n) / r]

Where PV is the present value, C is the cash flow each year, r is the interest rate, and n is the number of periods.

Plugging in the numbers:

PV = 100 * [(1 - (1+0.1)^-2) / 0.1] + 100 * [(1 - (1+0.1)^-1) / 0.1] 
PV = $181.82

For Year 3, we can use the present value of a single payment formula:

PV = C / (1 + r)^n

Plugging in the numbers:

PV = 200 / (1 + 0.12)^3 
PV = $128.96

Adding up the present values of all the payments gives us the total present value:

PV = $181.82 + $181.82 + $128.96 
PV = $492.60

Therefore, the answer is C) $453, rounded to the nearest dollar.

Assume Your Uncle Will Pay You $100 for Each of the Next