Final answer:
The problem with discount interest in the scenario is that the lender deducts the interest from the loan amount upfront, causing an effectively higher interest rate than stated. Proper calculations of simple interest are exemplified by three provided examples. They illustrate how loans, interest rates, and discount rates affect the total interest and present value of financial instruments.
Step-by-step explanation:
The scenario described is an example of discount interest where the lender subtracts the total interest from the loan amount up front. In the example, with a loan amount of $18,000 and an interest rate of 13.5%, the lender calculates the interest as $2,430 and deducts it immediately, providing $15,570 to the borrower. However, this practice is incorrect because it misrepresents the actual amount borrowed. The borrower only receives $15,570 but is charged interest as if $18,000 was received. This results in an effectively higher interest rate than the stated 13.5%.
Here's how simple interest calculations should work:
- Example 1: A $5,000 loan at a simple interest rate of 6% over three years would accumulate a total of $900 in interest ($5,000 x 0.06 x 3).
- Example 2: If $500 in simple interest is received on a $10,000 loan over five years, the interest rate charged is 1% ($500 / ($10,000 x 5)).
- Example 3: For a two-year bond with a face value of $3,000 and an 8% interest rate, the bond would pay $240 each year in interest. If the discount rate is the same as the bond's interest rate (8%), the present value of the bond is calculated using the present value formula which accounts for the receipt of two $240 interest payments and the $3,000 return of principal at the end of the second year. Recalculating with an 11% discount rate changes the bond's present value, reflecting the current value of receiving those future payments.