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QuestionCalculate the total interest for two loans of \$2,500: Loan A (3 years, 15\%, \$86.66/month) and Loan B (5 years, 10\%, \$53.12/month). Find the absolute difference, rounding to the nearest ten dollars.

Studdy Solution

STEP 1

Assumptions1. The principal amount for both loans is ,500.LoanAhasanannualinterestrateof15,500. Loan A has an annual interest rate of15% and is to be repaid in3 years with monthly repayments of 86.663. Loan B has an annual interest rate of10% and is to be repaid in5 years with monthly repayments of $53.124. The interest is calculated as a one-time payment, not monthly compounding5. We need to calculate the absolute difference between the total interest paid on both loans

STEP 2

First, we need to calculate the total payment made for each loan. This can be done by multiplying the monthly repayment by the total number of months.
Total payment=Monthly repaymenttimesTotal number of monthsTotal\, payment = Monthly\, repayment \\times Total\, number\, of\, months

STEP 3

Now, plug in the given values for the monthly repayment and total number of months for Loan A to calculate the total payment.
Total paymentA=$86.66times(3times12)Total\, payment_{A} = \$86.66 \\times (3 \\times12)

STEP 4

Calculate the total payment for Loan A.
Total paymentA=$86.66times36=$3,119.76Total\, payment_{A} = \$86.66 \\times36 = \$3,119.76

STEP 5

Repeat the process for Loan B.
Total paymentB=$53.12times(5times12)Total\, payment_{B} = \$53.12 \\times (5 \\times12)

STEP 6

Calculate the total payment for Loan B.
Total paymentB=$53.12times60=$3,187.20Total\, payment_{B} = \$53.12 \\times60 = \$3,187.20

STEP 7

Now that we have the total payments for both loans, we can calculate the total interest paid on each loan. This can be done by subtracting the principal amount from the total payment.
Total interest=Total payment−Principal amountTotal\, interest = Total\, payment - Principal\, amount

STEP 8

Plug in the values for the total payment and the principal amount for Loan A to calculate the total interest.
Total interestA=$3,119.76−$2,500Total\, interest_{A} = \$3,119.76 - \$2,500

STEP 9

Calculate the total interest for Loan A.
Total interestA=$3,119.76−$2,500=$619.76Total\, interest_{A} = \$3,119.76 - \$2,500 = \$619.76

STEP 10

Repeat the process for Loan B.
Total interestB=$3,187.20−$2,500Total\, interest_{B} = \$3,187.20 - \$2,500

STEP 11

Calculate the total interest for Loan B.
Total interestB=$3,187.20−$,500=$687.20Total\, interest_{B} = \$3,187.20 - \$,500 = \$687.20

STEP 12

Now that we have the total interest for both loans, we can calculate the absolute difference between them.
Absolute difference=∣Total interestA−Total interestB∣Absolute\, difference = |Total\, interest_{A} - Total\, interest_{B}|

STEP 13

Plug in the values for the total interest of both loans to calculate the absolute difference.
Absolute difference=∣$619.76−$687.20∣Absolute\, difference = |\$619.76 - \$687.20|

STEP 14

Calculate the absolute difference.
Absolute difference=∣$619.76−$687.20∣=$67.44Absolute\, difference = |\$619.76 - \$687.20| = \$67.44

STEP 15

Finally, round the absolute difference to the nearest ten dollars.
The absolute difference between the total interest paid on both loans is approximately $70 when rounded to the nearest ten dollars.

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