You buy a house from your brother and promise to pay him the $25,000 down payment in 2 years with 1.25% simple interest. You decide to pay off the down payment early, in one year. What amount will settle the debt if money can earn 0.75%?
To determine the amount that will settle the debt early, we can use the formula for calculating simple interest:
Simple Interest = Principal × Interest Rate × Time
In this case, the principal is $25,000, the interest rate is 1.25%, and the time is two years. However, since the debt is settled early, we need to calculate the interest for one year.
Using the formula, we can calculate the interest:
Interest = $25,000 × 1.25% × 1 year = $312.50
Now, we need to determine the amount that will settle the debt. Since you are paying off the down payment early and the money you have can earn 0.75% interest, we need to factor in this opportunity cost.
To calculate the settlement amount, we can use the formula for present value of a future sum:
Present Value = Future Value / (1 + Interest Rate) ^ Time
In this case, the future value is the principal plus the interest ($25,000 + $312.50 = $25,312.50), the interest rate is 0.75%, and the time is one year.
Using the formula, we can calculate the settlement amount:
Present Value = $25,312.50 / (1 + 0.75%)^1 ≈ $25,134.02
Therefore, the amount that will settle the debt early is approximately $25,134.02.