Question

katherine invests $7,770 in a six-month money market account giving 5.8% simple annual interest and $12,500 in a three-year cd giving 7.25% simple annual interest. assuming that katherine does not reinvest or renew these investments, how much money will she have when both investments reach maturity, to the nearest dollar
a. $2,944
b. $15,219
c. $23,214
d. $30,886

please select the best answer from the choices provided

○ a
○ b
○ c
○ d

Explanation:

Step1: Recall simple interest formula

The formula for simple interest is $I = P \times r \times t$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal), and $t$ is the time in years. Then the total amount $A$ is $A = P + I$.

Step2: Calculate interest for the money market account

For the money market account:

• $P_1 = 7770$ dollars,
• $r_1 = 5.8\% = 0.058$,
• $t_1 = 6$ months $= \frac{6}{12} = 0.5$ years.

Using the simple interest formula: $I_1 = P_1 \times r_1 \times t_1 = 7770 \times 0.058 \times 0.5$.

First, calculate $7770 \times 0.058 = 7770 \times \frac{58}{1000} = \frac{7770 \times 58}{1000} = \frac{450660}{1000} = 450.66$.

Then, $I_1 = 450.66 \times 0.5 = 225.33$ dollars.

The total amount for the money market account: $A_1 = P_1 + I_1 = 7770 + 225.33 = 7995.33$ dollars.

Step3: Calculate interest for the CD

For the CD:

• $P_2 = 12500$ dollars,
• $r_2 = 7.25\% = 0.0725$,
• $t_2 = 3$ years.

Using the simple interest formula: $I_2 = P_2 \times r_2 \times t_2 = 12500 \times 0.0725 \times 3$.

First, calculate $12500 \times 0.0725 = 12500 \times \frac{725}{10000} = \frac{12500 \times 725}{10000} = \frac{9062500}{10000} = 906.25$.

Then, $I_2 = 906.25 \times 3 = 2718.75$ dollars.

The total amount for the CD: $A_2 = P_2 + I_2 = 12500 + 2718.75 = 15218.75$ dollars.

Step4: Calculate the total amount when both investments mature

The total amount $A = A_1 + A_2 = 7995.33 + 15218.75 = 23214.08$ dollars, which is approximately 23214 dollars when rounded to the nearest dollar.

Answer:

c. $23,214$