Patricia and Joe Payne are divorced. The divorce settlement stipulated that Joe pay $520 a month for their daughter Suzanne until she turns 18 in 3 years. Interest is 18% a year. How much must Joe set aside today to meet the settlement?
To calculate the amount that Joe must set aside today to meet the settlement, we need to take into account the monthly payments, the duration of the payments, and the interest rate.
Let's break down the problem step by step:
Step 1: Find the future value of the monthly payments.
The monthly payment is $520, and the duration of the payments is 3 years. Since there are 12 months in a year, the total number of monthly payments over 3 years is 3 * 12 = 36.
To find the future value of the monthly payments, we can use the formula for the future value of an ordinary annuity:
FV = P * [(1 + r)^n - 1] / r
Where:
FV = Future value
P = Monthly payment
r = Interest rate per period
n = Number of periods
In this case, the monthly payment is $520, the interest rate per period is 18% / 12 = 0.015 (since the interest is given annually), and the number of periods is 36.
FV = $520 * [(1 + 0.015)^36 - 1] / 0.015
Let's calculate the future value.
FV = $520 * [1.015^36 - 1] / 0.015
FV ≈ $18,579.23
Step 2: Find the present value of the future payments.
Since we want to find the amount that Joe must set aside today, we need to determine the present value of the future payments.
The formula for the present value of an ordinary annuity is:
PV = FV / (1 + r)^n
In this case, the future value we calculated in step 1 is $18,579.23, the interest rate per period is 18% / 12 = 0.015, and the number of periods is 36.
PV = $18,579.23 / (1 + 0.015)^36
Let's calculate the present value.
PV = $18,579.23 / 1.015^36
PV ≈ $12,470.03
Therefore, Joe must set aside approximately $12,470.03 today to meet the settlement.