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QuestionGreg borrowed \$29,000 at 7.1\% for 1 year. Find: (a) monthly payment, (b) total repayment, (c) total interest paid.

Studdy Solution

STEP 1

Assumptions1. The borrowed amount is $29,000. The interest rate is7.1%
3. The time for repayment is1 year (12 months)
4. The loan is amortized, meaning the payments are made in regular installments and each payment includes both principal and interest5. The interest is compounded monthly

STEP 2

First, we need to find the monthly interest rate. We can do this by dividing the annual interest rate by the number of months in a year.
Monthly interest rate=Annual interest rate/Number of months in a yearMonthly\, interest\, rate = Annual\, interest\, rate / Number\, of\, months\, in\, a\, year

STEP 3

Now, plug in the given values for the annual interest rate and the number of months in a year to calculate the monthly interest rate.
Monthly interest rate=7.1%/12Monthly\, interest\, rate =7.1\% /12

STEP 4

Convert the percentage to a decimal value.
7.1%=0.0717.1\% =0.071Monthly interest rate=0.071/12Monthly\, interest\, rate =0.071 /12

STEP 5

Calculate the monthly interest rate.
Monthly interest rate=0.071/12=0.005925Monthly\, interest\, rate =0.071 /12 =0.005925

STEP 6

Now, we can calculate Greg's monthly payment using the formula for the monthly payment of an amortized loanMonthly payment=×r(1+r)n(1+r)n−1Monthly\, payment = \times \frac{r(1 + r)^n}{(1 + r)^n -1}where is the principal amount, r is the monthly interest rate, and n is the number of payments.

STEP 7

Plug in the values for the principal amount, the monthly interest rate, and the number of payments to calculate the monthly payment.
Monthly payment=$29,000×0.005925(1+0.005925)12(1+0.005925)12−1Monthly\, payment = \$29,000 \times \frac{0.005925(1 +0.005925)^{12}}{(1 +0.005925)^{12} -1}

STEP 8

Calculate the monthly payment amount.
Monthly payment=$29,000×0.005925(1+0.005925)12(1+0.005925)12−1=$2,487.70Monthly\, payment = \$29,000 \times \frac{0.005925(1 +0.005925)^{12}}{(1 +0.005925)^{12} -1} = \$2,487.70(a) Greg's monthly payment is $2,487.70.

STEP 9

Now that we have the monthly payment, we can find the total amount Greg has to repay the loan. This is simply the monthly payment times the number of payments.
Total amount to repay=Monthly payment×Number of paymentsTotal\, amount\, to\, repay = Monthly\, payment \times Number\, of\, payments

STEP 10

Plug in the values for the monthly payment and the number of payments to calculate the total amount to repay.
Total amount to repay=$2,487.70×12Total\, amount\, to\, repay = \$2,487.70 \times12

STEP 11

Calculate the total amount to repay.
Total amount to repay=$,487.70×=$29,852.40Total\, amount\, to\, repay = \$,487.70 \times = \$29,852.40(b) Greg's total amount to repay the loan is $29,852.40.

STEP 12

Finally, we can find the total amount of interest Greg will pay. This is simply the total amount to repay minus the original borrowed amount.
Total interest=Total amount to repay−Borrowed amountTotal\, interest = Total\, amount\, to\, repay - Borrowed\, amount

STEP 13

Plug in the values for the total amount to repay and the borrowed amount to calculate the total interest.
Total interest=$29,852.40−$29,000Total\, interest = \$29,852.40 - \$29,000

STEP 14

Calculate the total interest.
Total interest=$29,852.40−$29,000=$852.40Total\, interest = \$29,852.40 - \$29,000 = \$852.40(c) Greg's total amount of interest he will pay is $852.40.

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