Question

Compute the present value of $1,500 paid in three years using the following discount rates: 5 percent in the first year, 6 percent in the second year, and 7 percent in the third year. (Do not round intermediate calculations. Round your answer to 2 decimal places.).

Answer 1

The present value of $1,500 paid in three years with respective discount rates of 5%, 6%, and 7% per year, calculated sequentially, is $1,259.18 when rounded to two decimal places.

Step-by-step explanation:

To compute the present value of $1,500 paid in three years with varying discount rates for each year, we apply these rates accordingly for each of the three years sequentially.

For the first year at 5%, the formula is: PV1 = FV / (1 + r1), where PV1 is the present value after the first year, FV is the future value, and r1 is the first-year discount rate.

For the second year at 6%, the calculation is based on the first year's present value PV1, and the formula is: PV2 = PV1 / (1 + r2).

For the third year at 7%, the formula is: PV3 = PV2 / (1 + r3). Once we have the present value for the third year PV3, that is the final present value of the $1,500 paid in three years.

We first calculate the present value after one year: $1,500 / (1 + 0.05) = $1,500 / 1.05 = $1,428.57 (Do not round intermediate calculations).

Then, we calculate the present value after two years: $1,428.57 / (1 + 0.06) = $1,428.57 / 1.06 = $1,347.72.

Finally, the present value after three years using a 7% discount rate for the third year: $1,347.72 / (1 + 0.07) = $1,347.72 / 1.07 = $1,259.18. Rounding the final answer to two decimal places, the present value is $1,259.18.

Answer 2

The present value of $1,500 paid in three years is $1259.54

Step-by-step explanation:

A = P(1 + r/100)^n

where :

A is the future value

P is the present value

r is the rate of interest

n is the time period.

1500 = P*(1.05)*(1.06)*(1.07)

P = 1500/1.19091

= $1259.54

Therefore, The present value of $1,500 paid in three years is $1259.54