Questions: Isabel received a 1300 bonus. She decided to invest it in a 3-year certificate of deposit (CD) with an annual interest rate of 1.31% compounded monthly. 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 Isabel's account after 3 years? (b) How much interest is earned on Isabel's investment after 3 years?

Isabel received a 1300 bonus. She decided to invest it in a 3-year certificate of deposit (CD) with an annual interest rate of 1.31% compounded monthly.
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 Isabel's account after 3 years?

(b) How much interest is earned on Isabel's investment after 3 years?

Transcript text: Isabel received a $1300 bonus. She decided to invest it in a 3-year certificate of deposit (CD) with an annual interest rate of $1.31\%$ compounded monthly. 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 Isabel's account after 3 years? $\$ \square$ (b) How much interest is earned on Isabel's investment after 3 years? $\$ \square$

Solution

Solution Steps

Step 1: Calculate the Future Value

To find the future value $A$ of an investment, we use the formula $A = P(1 + \frac{r}{n})^{nt}$, where:

$P$ is the principal amount or the initial investment, which is 1300.
$r$ is the annual interest rate in decimal form, which is 0.0131.
$n$ is the number of times the interest is compounded per year, which is 12.
$t$ is the time the money is invested for in years, which is 3. Substituting the given values into the formula, we get $A = 1300 \times (1 + \frac{0.0131}{12})^{12\times3}$. After performing the calculations, the future value $A$ is approximately 1352.08.

Step 2: Calculate the Interest Earned

The interest earned can be found by subtracting the principal $P$ from the future value $A$, i.e., \[ \text{Interest Earned} = A - P = 1352.08 - 1300 \] After performing the subtraction, the interest earned is approximately 52.08.