Final answer:
To solve the loan problem, we calculate the discount, the amount of money received, and the true interested rate. The discount is found using the formula for simple interest, and the true interest rate accounts for the fact that the loan is discounted up front.
Step-by-step explanation:
The student's question pertains to calculating the discount, the amount of money received, and the true interest rate of a discounted loan with principal (P) of $1770, a nominal interest rate (r) of 5.5%, and a time (t) of 7 years. We approach this problem using the formulas for simple interest and discounts
- The discount on the loan is found using the formula Discount = P × r × t, which gives us the total amount of interest that will be subtracted from the principal upfront
- To calculate the amount of money received, we subtract the discount from the principal: Amount received = P - Discount
- The true interest rate can be calculated by considering the annual interest compared with the actual amount received, which differs from the nominal rate since the loan is discounted at the beginning
To answer the student's question:
- The discount (a) would be $677.25 ($1770 × 0.055 × 7).
- The amount of money received (b) would be $1092.75 ($1770 - $677.25).
- The true interest rate (c) can be calculated by taking the discount divided by the amount received and then divided by the time, which would then need to be converted into a percentage.
It's critical to note that exact calculations for the true interest rate would require more specifics about the compounding of the discount which are not provided in the question.