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QuestionArjun needs a \350,000loanfor20yearsat4.2%interest,compoundedmonthly.Findhismonthlyrepaymentofabout350,000 loan for 20 years at 4.2\% interest, compounded monthly. Find his monthly repayment of about 2160$.

Studdy Solution

STEP 1

Assumptions1. The loan amount is $350,000. The interest rate is4.% per annum3. The time for repayment is20 years4. The interest is compounded monthly5. Arjun will make equal monthly payments

STEP 2

First, we need to convert the annual interest rate to a monthly interest rate. We can do this by dividing the annual interest rate by12.
Monthly Interest Rate=Annual Interest Rate/12Monthly\, Interest\, Rate = Annual\, Interest\, Rate /12

STEP 3

Now, plug in the given values for the annual interest rate to calculate the monthly interest rate.
Monthly Interest Rate=.2%/12Monthly\, Interest\, Rate =.2\% /12

STEP 4

Convert the percentage to a decimal value.
4.2%=0.0424.2\% =0.042Monthly Interest Rate=0.042/12Monthly\, Interest\, Rate =0.042 /12

STEP 5

Calculate the monthly interest rate.
Monthly Interest Rate=0.042/12=0.0035Monthly\, Interest\, Rate =0.042 /12 =0.0035

STEP 6

Now, we need to find the total number of payments Arjun will make. This is the number of years times the number of months in a year.
Total Payments=Years of RepaymenttimesMonths in a YearTotal\, Payments = Years\, of\, Repayment \\times Months\, in\, a\, Year

STEP 7

Plug in the values for the years of repayment and the number of months in a year to calculate the total payments.
Total Payments=20times12Total\, Payments =20 \\times12

STEP 8

Calculate the total number of payments.
Total Payments=20times12=240Total\, Payments =20 \\times12 =240

STEP 9

Now, we can calculate the monthly payment using the formula for the monthly payment on a loan with compound interestMonthly Payment=Loan AmounttimesMonthly Interest Ratetimes(+Monthly Interest Rate)Total Payments(+Monthly Interest Rate)Total Payments−Monthly\, Payment = Loan\, Amount \\times \frac{Monthly\, Interest\, Rate \\times ( + Monthly\, Interest\, Rate)^{Total\, Payments}}{( + Monthly\, Interest\, Rate)^{Total\, Payments} -}

STEP 10

Plug in the values for the loan amount, the monthly interest rate, and the total number of payments into the formula.
Monthly Payment=$350,000times0.0035times(+0.0035)240(+0.0035)240−Monthly\, Payment = \$350,000 \\times \frac{0.0035 \\times ( +0.0035)^{240}}{( +0.0035)^{240} -}

STEP 11

Calculate the monthly payment amount.
Monthly Payment≈$2160Monthly\, Payment \approx \$2160Arjun's minimum monthly repayments are approximately $2160.

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