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QuestionElise has two loans: a \$20,000 fixed-rate at 4.5\% and a \$20,000 variable-rate at 4.15\%. Which is more predictable in total cost?

Studdy Solution

STEP 1

Assumptions1. The first loan amount is 20,000withafixedinterestrateof4.520,000 with a fixed interest rate of4.5% for15 years. The second loan amount is also 20,000 but with a variable interest rate of4.15% for15 years3. The interest is calculated annually, not monthly compounding4. The total amount to be paid includes both the principal amount and the interest

STEP 2

For a fixed-rate loan, the total amount to be paid can be calculated by adding the interest to the principal amount. The interest can be calculated using the formulaInterest=Principal amounttimesInterest ratetimesTimeInterest = Principal\, amount \\times Interest\, rate \\times Time

STEP 3

Now, plug in the given values for the first loan's principal amount, interest rate, and time to calculate the interest.
Interest=$20,000times.5%times15Interest = \$20,000 \\times.5\% \\times15

STEP 4

Convert the percentage to a decimal value.
4.%=0.0454.\% =0.045Interest=$20,000times0.045times15Interest = \$20,000 \\times0.045 \\times15

STEP 5

Calculate the interest amount for the first loan.
Interest=$20,000times0.045times15=$13,500Interest = \$20,000 \\times0.045 \\times15 = \$13,500

STEP 6

Now that we have the interest amount, we can find the total amount Elise has to pay back for the first loan. This includes both the borrowed amount and the interest.
Total amount=Principal amount+InterestTotal\, amount = Principal\, amount + Interest

STEP 7

Plug in the values for the first loan's principal amount and the interest to calculate the total amount.
Total amount=$20,000+$13,500Total\, amount = \$20,000 + \$13,500

STEP 8

Calculate the total amount Elise has to pay back for the first loan.
Total amount=$20,000+$13,500=$33,500Total\, amount = \$20,000 + \$13,500 = \$33,500

STEP 9

For a variable-rate loan, the total amount to be paid cannot be accurately predicted because the interest rate may change over time. Therefore, we cannot calculate the exact interest and total amount for the second loan.

STEP 10

Comparing the two loans, Elise can more accurately predict the total amount she will have to pay for the first loan because it has a fixed interest rate. The total amount for the second loan cannot be accurately predicted because it has a variable interest rate.
Elise can more accurately predict the total amount she will have to pay for the first loan.

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