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 calculate the amount that will settle the debt, we need to use the formula for simple interest:
I = P * R * T
Where:
I = interest
P = principal amount (the down payment)
R = interest rate
T = time (in years)
In this case, the principal amount (P) is $25,000, the interest rate (R) is 1.25%, and the time (T) is 1 year.
First, we can calculate the interest accumulated over one year:
I = $25,000 * 1.25% * 1
I = $312.50
Now, to settle the debt, we need to add this interest to the principal amount:
Total Debt = Principal amount + Interest accumulated
Total Debt = $25,000 + $312.50
Total Debt = $25,312.50
To find the amount that will settle the debt, we need to consider the opportunity cost of the money had it been invested at a 0.75% interest rate. This means that if you had invested the $25,000 at 0.75% instead of paying off the down payment early, it would have earned interest.
To calculate the interest earned:
Interest earned = Principal amount * Interest rate * Time
Interest earned = $25,000 * 0.75% * 1
Interest earned = $187.50
Finally, we subtract the interest earned from the total debt to find the amount that will settle the debt:
Amount to settle the debt = Total Debt - Interest earned
Amount to settle the debt = $25,312.50 - $187.50
Amount to settle the debt = $25,125.00
Therefore, the amount that will settle the debt is $25,125.00.