On January 5, Ebony Davis borrowed $6,500 on a simple interest loan from a lending institution to finance her catering business. She borrows the money at a rate of 8.5% with a term ending on December 9.
a. Calculate Ebony's interest on the simple interest loan if she waits until the full term to pay back the loan.
b. If Ebony makes payments of $1500 on May 3 and $2500 on September 11,
how much will she have left to pay on December 9?
c. How much money does she save by making the payments instead of waiting to the end to repay the loan?
Solved under a later post.
a. To calculate Ebony's interest on the simple interest loan if she waits until the full term to pay back the loan, we can use the formula:
Interest = Principal × Rate × Time
Where:
- Principal is the amount borrowed ($6,500)
- Rate is the annual interest rate (8.5% or 0.085 as a decimal)
- Time is the length of the loan term in years (from January 5 to December 9 is approximately 11 months)
First, we need to convert the time to years:
Time = 11 months / 12 months/year = 0.92 years
Now we can calculate the interest:
Interest = $6,500 × 0.085 × 0.92 = $501.40
Therefore, the interest on the simple interest loan if Ebony waits until the full term to pay back the loan is $501.40.
b. To calculate how much Ebony will have left to pay on December 9 after making payments of $1500 on May 3 and $2500 on September 11, we need to subtract the total payments made from the principal loan amount.
Total payments made = $1500 + $2500 = $4000
Remaining principal = Principal - Total payments made = $6,500 - $4000 = $2500
Therefore, Ebony will have $2500 left to pay on December 9.
c. To calculate how much money Ebony saves by making the payments instead of waiting until the end to repay the loan, we need to compare the total interest paid in both scenarios.
Total interest paid if Ebony waits until the end = $501.40 (calculated in part a)
Total interest paid if Ebony makes payments = Interest on remaining principal after each payment
Interest on remaining principal after the first payment:
Interest = Remaining principal after first payment × Rate × Time
Time = 8 months / 12 months/year = 0.67 years
Interest = $2500 × 0.085 × 0.67 = $142.92
Remaining principal after the first payment = Principal - First payment = $6,500 - $1500 = $5000
Interest on remaining principal after the second payment:
Interest = Remaining principal after second payment × Rate × Time
Time = 3 months / 12 months/year = 0.25 years
Interest = $5000 × 0.085 × 0.25 = $106.25
Total interest paid if Ebony makes payments = $142.92 + $106.25 = $249.17
Therefore, Ebony saves $501.40 - $249.17 = $252.23 by making the payments instead of waiting until the end to repay the loan.