Kate will receive $300 next year, $500 two years from now, and $1000 three years from now. All payments are received at the end of the year. At a 7% rate of return, we need to calculate the total worth of these payments to Kate at the end of the three years.

1. Problem Description

Kate will receive $300 next year,$500 two years from now, and $1000 three years from now. All payments are received at the end of the year. At a 7% rate of return, we need to calculate the total worth of these payments to Kate at the end of the three years.

2. Solution Steps

First, we calculate the future value of each payment at the end of the third year using the future value formula:

$FV = PV (1 + r)^n$

where:

$FV$ is the future value.

$PV$ is the present value (payment amount).

$r$ is the interest rate (7% or 0.07).

$n$ is the number of years until the end of year

3.

Payment 1: $300 received in 1 year. It grows for 2 years (3-1=2).

$FV_1 = 300 (1 + 0.07)^2 = 300 (1.07)^2 = 300 * 1.1449 = 343.47$

Payment 2: $500 received in 2 years. It grows for 1 year (3-2=1).

$FV_2 = 500 (1 + 0.07)^1 = 500 (1.07) = 535$

Payment 3: $1000 received in 3 years. It grows for 0 years (3-3=0).

$FV_3 = 1000 (1 + 0.07)^0 = 1000 (1) = 1000$

Finally, sum the future values of all three payments to find the total worth at the end of the three years:

$Total FV = FV_1 + FV_2 + FV_3 = 343.47 + 535 + 1000 = 1878.47$

3. Final Answer

$1878.47