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QuestionBea can spend $200\$ 200 monthly on a $22,500\$ 22,500 loan at 6%6\%. Check if 12-year or 20-year loans fit her budget.

Studdy Solution

STEP 1

Assumptions1. The maximum amount Bea can spend per month on the student loan is 200.TheloanamountBeaneedsis200. The loan amount Bea needs is 22,5003. The interest rate for both loan options is6%
4. The first loan option has a term of12 years5. The second loan option has a term of20 years6. The interest is calculated as a one-time payment, not monthly compounding7. Both the principal amount and interest must be equally divided among the loan term

STEP 2

First, we need to find the interest amount on the borrowed sum for each loan option. We can do this by multiplying the borrowed amount by the interest rate.
Interest=Borrowed amounttimesInterest rateInterest = Borrowed\, amount \\times Interest\, rate

STEP 3

Now, plug in the given values for the borrowed amount and interest rate to calculate the interest.
Interest=$22,500times6%Interest = \$22,500 \\times6\%

STEP 4

Convert the percentage to a decimal value.
6%=0.066\% =0.06Interest=$22,500times0.06Interest = \$22,500 \\times0.06

STEP 5

Calculate the interest amount.
Interest=$22,500times0.06=$1,350Interest = \$22,500 \\times0.06 = \$1,350

STEP 6

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

STEP 7

Plug in the values for the borrowed amount and the interest to calculate the total amount.
Total amount=$22,500+$1,350Total\, amount = \$22,500 + \$1,350

STEP 8

Calculate the total amount Bea has to pay back.
Total amount=$22,500+$1,350=$23,850Total\, amount = \$22,500 + \$1,350 = \$23,850

STEP 9

Now that we have the total amount Bea has to pay back, we can divide this by the number of months in each loan term to find the monthly payment for each loan option.
Monthly payment=Total amount/Number of monthsMonthly\, payment = Total\, amount / Number\, of\, months

STEP 10

Plug in the values for the total amount and the number of months for the first loan option to calculate the monthly payment.
Monthly payment=$23,850/(12times12)Monthly\, payment = \$23,850 / (12 \\times12)

STEP 11

Calculate the monthly payment amount for the first loan option.
Monthly payment=$23,850/144=$165.63Monthly\, payment = \$23,850 /144 = \$165.63

STEP 12

Repeat steps10 and11 for the second loan option.
Monthly payment=$23,850/(20times12)Monthly\, payment = \$23,850 / (20 \\times12)Monthly payment=$23,850/240=$99.38Monthly\, payment = \$23,850 /240 = \$99.38Both loan options fit within Bea's budget of $200 per month.

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