William borrowed $\$20000$ from a bank. The interest rate was $12\%$ p.a. The interest was compounded monthly. He repaid $\$2000$ after each settlement at the end of the month. After $2$ repayments, how much did he owe the bank? $\newline$ A. $\$16382$ $\newline$ B. $\$18000$ $\newline$ C. $\$18200$ $\newline$ D. $\$18382$

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Q. William borrowed

\$20000

from a bank. The interest rate was

12\%

p.a. The interest was compounded monthly. He repaid

\$2000

after each settlement at the end of the month. After

2

repayments, how much did he owe the bank?

\newline

\$16382

\newline

\$18000

\newline

\$18200

\newline

\$18382

Calculate Monthly Interest Rate: Calculate the monthly interest rate. $\newline$ The annual interest rate is $12\%$ , so the monthly interest rate is $12\%$ divided by $12$ months. $\newline$ Monthly interest rate = $\frac{12\%}{12} = 1\%$ $\newline$ Convert the percentage to a decimal for calculations. $\newline$ Monthly interest rate = $1\% = 0.01$
Calculate Amount After First Month: Calculate the amount owed after the first month before repayment. $\newline$ The interest is compounded monthly, so we apply the monthly interest rate to the principal. $\newline$ Amount after first month = Principal amount $\times$ $(1 + \text{Monthly interest rate})$ $\newline$ Amount after first month = $\$20,000 \times (1 + 0.01)$ $\newline$ Amount after first month = $\$20,000 \times 1.01$ $\newline$ Amount after first month = $\$20,200$
Calculate Amount After First Repayment: Calculate the amount owed after the first repayment. $\newline$ William repays $\$2,000$ at the end of the first month. $\newline$ Amount after first repayment = Amount after first month - Repayment amount $\newline$ Amount after first repayment = $\$20,200$ - $\$2,000$ $\newline$ Amount after first repayment = $\$18,200$
Calculate Amount After Second Month: Calculate the amount owed after the second month before repayment. $\newline$ Again, apply the monthly interest rate to the new principal. $\newline$ Amount after second month = Amount after first repayment $\times$ $(1 + \text{Monthly interest rate})$ $\newline$ Amount after second month = $\$18,200 \times (1 + 0.01)$ $\newline$ Amount after second month = $\$18,200 \times 1.01$ $\newline$ Amount after second month = $\$18,382$
Calculate Amount After Second Repayment: Calculate the amount owed after the second repayment. $\newline$ William repays $\$2,000$ at the end of the second month. $\newline$ Amount after second repayment = Amount after second month - Repayment amount $\newline$ Amount after second repayment = $\$18,382$ - $\$2,000$ $\newline$ Amount after second repayment = $\$16,382$