Miss Yu takes out a home loan of $360,000 at 5% per annum for 30 years. We need to calculate her monthly loan repayment using the table provided and then calculate the total amount she repays over 30 years. The table shows the monthly repayment per $1000 borrowed.

Applied MathematicsFinancial MathematicsLoansCompound InterestCalculations
2025/5/27

1. Problem Description

Miss Yu takes out a home loan of 360,000at5360,000 at 5% per annum for 30 years. We need to calculate her monthly loan repayment using the table provided and then calculate the total amount she repays over 30 years. The table shows the monthly repayment per 1000 borrowed.

2. Solution Steps

a) Calculate Miss Yu's monthly loan repayment.
First, we need to find the monthly repayment per 1000borrowedfromthetable.Theloantermis30yearsandtheinterestrateis51000 borrowed from the table. The loan term is 30 years and the interest rate is 5%. From the table, the monthly repayment is 5.37 per $1000 borrowed.
Next, we need to determine how many thousands of dollars Miss Yu borrowed:
Loan Amount = \360,000$
Amount per unit = \1,000$
Number of units = \frac{\360,000}{\1,000} = 360
Now, we multiply the number of units by the monthly repayment per $1000:
MonthlyRepayment=Numberofunits×RepaymentperunitMonthly Repayment = Number of units \times Repayment per unit
Monthly Repayment = 360 \times \5.37 = \1933.201933.20
b) Calculate the total amount she repays over 30 years.
TotalNumberofmonths=30 years×12 months/year=360 monthsTotal Number of months = 30 \ years \times 12 \ months/year = 360 \ months
TotalRepayment=MonthlyRepayment×TotalNumberofMonthsTotal Repayment = Monthly Repayment \times Total Number of Months
Total Repayment = \1933.20 \times 360 = \695,952695,952

3. Final Answer

a) Miss Yu's monthly loan repayment is $1933.
2

0. b) The total amount that she repays is $695,952.

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