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?
Jan. 5th through Dec. 9th = 338 Days.
a. I = Po*r*t = 6500*(0.085/360)*338 =
$518.74
b. P=(6500 + 6500*(0.085/360)*118)-1500
= $6681.10 - 1500 = $5181.10 After May 3.
P = 5181.10 + 5181.10*(0.085/360)*128 -
2500 = 5337.68 - 2500 = $2837.68 After
Sept. 11
P = 2837.68 + 2837.68*(0.085/360)*89 =
$2897.32 Due on Dec. 9.
c. Total Paid = 1500 + 2500 + 2897.32 =
$6897.32
I = 6897.32 - 6500 = $397.32
518.74 - 397.32 = $121.42 = Amt. saved.
Thanks Henry!
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 for simple interest:
Interest = Principal * Interest Rate * Time
Principal = $6,500
Interest Rate = 8.5% (0.085)
Time = (number of days) / 365 (since the interest rate is annual)
The term of the loan is from January 5 to December 9, which is a total of 339 days.
Now we can calculate the interest:
Interest = $6,500 * 0.085 * (339/365)
Interest = $491.23 (rounded to the nearest cent)
Therefore, Ebony's interest on the simple interest loan if she waits until the full term to pay back the loan is $491.23.
b. To calculate how much Ebony will have left to pay on December 9 after making the payments, we need to subtract the payments from the principal amount.
Principal = $6,500
Payment 1 = $1,500
Payment 2 = $2,500
Remaining Principal = Principal - Payment 1 - Payment 2
Remaining Principal = $6,500 - $1,500 - $2,500
Remaining Principal = $2,500
Therefore, Ebony will have $2,500 left to pay on December 9 after making the payments.
c. To calculate how much money Ebony saves by making the payments instead of waiting to repay the loan in full, we need to calculate the difference between the total interest paid if she waits and the total interest paid with the payments.
Total interest paid if waiting = Principal * Interest Rate * Time
Total interest paid with payments = (Principal - Payment 1 - Payment 2) * Interest Rate * Time
Using the values from part a and part b:
Total interest paid if waiting = $6,500 * 0.085 * (339/365)
Total interest paid with payments = $2,500 * 0.085 * (339/365)
Savings = Total interest paid if waiting - Total interest paid with payments
Savings = ($6,500 * 0.085 * (339/365)) - ($2,500 * 0.085 * (339/365))
Savings = $491.23 - $144.73
Savings = $346.50 (rounded to the nearest cent)
Therefore, Ebony saves $346.50 by making the payments instead of waiting to repay the loan in full.