Question

true or false: compound interest includes the interest that an investor earns on the original investment plus interest earned on the interest.
true
false
question 17
2 pts
if my beginning balance on my savings account is 1,000 and the interest amount is 7%, what is my year 1 ending balance using simple interest?
1070
700
1000
1007
question 18
2 pts
what annual interest rate will cause your money to double in 5 years?
14.4%
9%
17.4%
18%

Explanation:

First Question (True/False about Compound Interest)

Compound interest is calculated on the initial principal and also on the accumulated interest of previous periods. So it includes interest on the original investment and interest on the interest earned. Thus, the statement is true.

Step1: Recall Simple Interest Formula

The formula for simple interest is $I = P \times r \times t$, where $P$ is principal, $r$ is rate (in decimal), and $t$ is time. The ending balance $A$ is $A = P + I$.

Step2: Identify Values

$P = 1000$, $r = 7\% = 0.07$, $t = 1$.

Step3: Calculate Interest

$I = 1000 \times 0.07 \times 1 = 70$.

Step4: Calculate Ending Balance

$A = 1000 + 70 = 1070$.

Step1: Use Rule of 72 (Approximation)

The Rule of 72 states that the time to double (in years) is approximately $\frac{72}{\text{interest rate (in \%)}}$. We know time $t = 5$ years, so $5 \approx \frac{72}{r}$.

Step2: Solve for $r$

Rearranging, $r \approx \frac{72}{5} = 14.4\%$.

Answer:

A. True

Question 17 (Simple Interest Ending Balance)