find the total balance of each investment account earning simple annual interest. a: $624 at 5% for 3 years…

Explanation:

Step1: Recall simple - interest formula

The formula for simple interest 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. The total balance $A$ is $A=P + I=P(1 + rt)$.

Step2: Solve for A

For the first investment: $P = 624$, $r=0.05$, $t = 3$. $A=P(1+rt)=624\times(1 + 0.05\times3)$ $=624\times(1 + 0.15)$ $=624\times1.15$ $=717.6$

Step3: Solve for B

For the second investment: First convert 18 months to years. Since 1 year = 12 months, $t=\frac{18}{12}=1.5$ years, $P = 4120$, $r = 0.07$. $A=P(1+rt)=4120\times(1+0.07\times1.5)$ $=4120\times(1 + 0.105)$ $=4120\times1.105$ $=4552.6$

Step4: Solve for C

For the third investment: Convert 6 months to years. $t=\frac{6}{12}=0.5$ years, $P = 900$, $r=0.031$. $A=P(1+rt)=900\times(1+0.031\times0.5)$ $=900\times(1 + 0.0155)$ $=900\times1.0155$ $=913.95$

Step5: Solve for D

For the fourth investment: $P = 275$, $r=0.048$, $t = 8$. $A=P(1+rt)=275\times(1+0.048\times8)$ $=275\times(1 + 0.384)$ $=275\times1.384$ $=380.6$

Answer:

A: $717.6$ B: $4552.6$ C: $913.95$ D: $380.6$