suppose dan borrows $7500 at an interest rate of 18% compounded each year. assume that no payments are made…

Explanation:

Step1: Recall compound - interest formula

The compound - interest formula when compounded annually is $A = P(1 + r)^t$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), and $t$ is the number of years. Here, $P=$7500$, $r = 0.18$, and we will calculate $A$ for different values of $t$.

Step2: Calculate the amount owed at the end of 1 year

Substitute $P = 7500$, $r=0.18$, and $t = 1$ into the formula $A = P(1 + r)^t$. $A_1=7500\times(1 + 0.18)^1=7500\times1.18 = 8850$

Step3: Calculate the amount owed at the end of 2 years

Substitute $P = 7500$, $r = 0.18$, and $t = 2$ into the formula $A = P(1 + r)^t$. $A_2=7500\times(1 + 0.18)^2=7500\times1.18^2=7500\times1.3924 = 10443$

Answer:

(a) $8850$ (b) $10443$