4 find the interest earned: $26,000 for 36 months at 7.5% annual compound interest

Explanation:

Step1: Identify the formula

The compound - interest formula is $A = P(1 + \frac{r}{n})^{nt}$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), $n$ is the number of times interest is compounded per year, and $t$ is the number of years. Here, assume $n = 1$ (compounded annually). First, convert the time and rate to the correct form. The principal $P=$26000$, the annual interest rate $r = 7.5%=0.075$, and the time $t=\frac{36}{12}=3$ years.

Step2: Calculate the amount $A$

Substitute the values into the formula: $A = 26000(1 + 0.075)^{3}$. First, calculate the value inside the parentheses: $1+0.075 = 1.075$. Then, find $(1.075)^{3}=1.075\times1.075\times1.075 = 1.242296875$. Multiply by the principal: $A=26000\times1.242296875=$32299.72$.

Step3: Calculate the interest $I$

The interest $I$ is the difference between the final amount $A$ and the principal $P$. So, $I=A - P$. Substitute $A = 32299.72$ and $P = 26000$: $I=32299.72-26000=$6299.72$.

Answer:

$6299.72$