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A bank offers an investment account with an annual interest rate of compounded quarterly. Charmaine invests into the account for 2 years.
Answer the questions below. Do not round any intermediate computations, and round your final answers to the nearest cent. If necessary, refer to the
list of financial formulas.
(a) Assuming no withdrawals are made, how much money is in Charmaine’s
account after 2 years?
(b) How much interest is earned on Charmaine’s investment after 2 years?

Ask by Olson Rowe. in the United States

Mar 14,2025

Question

Try Again
Your answer is incorrect.
A bank offers an investment account with an annual interest rate of compounded quarterly. Charmaine invests into the account for 2 years.
Answer the questions below. Do not round any intermediate computations, and round your final answers to the nearest cent. If necessary, refer to the
list of financial formulas.
(a) Assuming no withdrawals are made, how much money is in Charmaine’s
account after 2 years?
(b) How much interest is earned on Charmaine’s investment after 2 years?

Ask by Olson Rowe. in the United States

Mar 14,2025

UpStudy AI · Accepted Answer

1. We start with the compound interest formula  
   $$
   A = P\left(1+\frac{r}{n}\right)^{nt},
   $$  
   where  
   - $$P=3700$$ is the initial principal,  
   - $$r=0.0113$$ is the annual interest rate (in decimal),  
   - $$n=4$$ is the number of compounding periods per year (quarterly), and  
   - $$t=2$$ is the number of years.

2. Substitute the values into the formula:  
   $$
   A = 3700\left(1+\frac{0.0113}{4}\right)^{4 \times 2}.
   $$

3. Compute the periodic interest rate:  
   $$
   \frac{0.0113}{4} = 0.002825.
   $$

4. The expression now becomes:  
   $$
   A = 3700\left(1+0.002825\right)^{8} = 3700\left(1.002825\right)^{8}.
   $$

5. Calculate the compound factor $$\left(1.002825\right)^{8}$$.  
   Using exact computation (without rounding intermediate steps), one finds  
   $$
   \left(1.002825\right)^{8} \approx 1.022823.
   $$

6. Now, compute the account value after 2 years:  
   $$
   A \approx 3700 \times 1.022823 \approx 3784.43.
   $$

7. Thus, the answers are:  
   (a) The amount in Charmaine's account after 2 years is  
   $$
   \$3784.43.
   $$  
   (b) The interest earned is the final amount minus the initial investment:  
   $$
   \text{Interest} = 3784.43 - 3700 = 84.43.
   $$

8. Therefore, Charmaine earns  
   $$
   \$84.43 \text{ in interest.}
   $$
After 2 years, Charmaine has \$3,784.43 in her account. She earns \$84.43 in interest.

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