Question

$1,000{(1+\frac{r}{1,200})}^{12}$
The expression above gives the amount of money, in dollars, generated in a year by a $\$1,000$ deposit in a bank account that pays an annual interest rate of $r\%$, compounded monthly. Which of the following expressions shows how much additional money is generated at an interest rate of $5\%$ than at an interest rate of $3\%$?

• A. $1,000{(1+\frac{5-3}{1,200})}^{12}$
• B. $1,000{(1+\frac{\frac{5}{3}}{1,200})}^{12}$
• C. $\frac{1,000{(1+\frac{5}{1,200})}^{12}}{1,000{(1+\frac{3}{1,200})}^{12}}$
• D. $1,000{(1+\frac{5}{1,200})}^{12}-1,000{(1+\frac{3}{1,200})}^{12}$

Answer 1

The correct option is D $1,000{(1+\frac{5}{1,200})}^{12}-1,000{(1+\frac{3}{1,200})}^{12}$

The amount generated when the interest rate is $5\%$ is given by $A_5=1000{(1+\frac{5}{1200})}^{12}$

Similarly, the amount generated when the interest rate is $3\%$ is given by $A_3=1000{(1+\frac{3}{1200})}^{12}$

Thus, the additional amount will be given by $A_5-A_3$

i.e. $1000{(1+\frac{5}{1200})}^{12}-1000{(1+\frac{3}{1200})}^{12}$