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You ask your friend to lend you $\$200$ to buy your favorite toy. She says she can lend you the money only if you give her an extra $\$2$ every month that passes before you return it. What is the total amount you must pay her if you return it after $2$ years? Also, what is the annual rate of interest she is charging you?

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Exponential growth and decay: word problems

Full solution

Q. You ask your friend to lend you

\$200

to buy your favorite toy. She says she can lend you the money only if you give her an extra

\$2

every month that passes before you return it. What is the total amount you must pay her if you return it after

2

years? Also, what is the annual rate of interest she is charging you?

Calculate Interest Total: Calculate the total interest after $2$ years. $\newline$ Reasoning: Interest is $\$2$ per month for $24$ months. $\newline$ Calculation: $\$2 \times 24 = \$48$ .
Calculate Amount Paid: Calculate the total amount to be paid after $2$ years. $\newline$ Reasoning: Add the total interest to the initial amount borrowed. $\newline$ Calculation: $\$200$ + $\$48$ = $\$248$ .
Calculate Annual Rate: Calculate the annual rate of interest. $\newline$ Reasoning: Find the total interest per year and divide by the initial amount, then convert to percentage. $\newline$ Calculation: $\left(\$48 / 2 \text{ years}\right) / \$200 \times 100 = 12\%$ .

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