katherine invests $7,770 in a six - month money market account giving 5.8% simple annual interest and…

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

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

Answer

Explanation:

Step1: Calculate interest for money - market account

The simple - interest formula is $I = Prt$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), and $t$ is the time in years. For the money - market account, $P_1=$7770$, $r_1 = 0.058$, and $t_1=\frac{6}{12}=0.5$ years. $I_1=P_1r_1t_1=7770\times0.058\times0.5 = 7770\times0.029=$225.33$ The amount in the money - market account at maturity, $A_1=P_1 + I_1=7770+225.33=$7995.33$

Step2: Calculate interest for CD

For the CD, $P_2 = $12500$, $r_2=0.0725$, and $t_2 = 3$ years. $I_2=P_2r_2t_2=12500\times0.0725\times3=12500\times0.2175=$2718.75$ The amount in the CD at maturity, $A_2=P_2 + I_2=12500 + 2718.75=$15218.75$

Step3: Calculate total amount

The total amount $A=A_1 + A_2=7995.33+15218.75=$23214.08\approx$23214$

Answer:

c. $$23,214$