mary borrowed $8000 at a rate of 14.5%, compounded quarterly. assuming she makes no payments, how much will…

Explanation:

Step1: Recall compound interest formula

The compound interest formula is $A = P(1 + \frac{r}{n})^{nt}$, where:

• $A$ is the amount of money accumulated after $n$ years, including interest.
• $P$ is the principal amount (the initial amount of money).
• $r$ is the annual interest rate (decimal).
• $n$ is the number of times that interest is compounded per year.
• $t$ is the time the money is invested for in years.

Given:

• $P = 8000$
• $r = 14.5% = 0.145$
• $n = 4$ (compounded quarterly)
• $t = 10$

Step2: Substitute values into formula

Substitute the values into the formula: $A = 8000(1 + \frac{0.145}{4})^{4 \times 10}$

First, calculate the exponent: $4 \times 10 = 40$

Then, calculate the rate per period: $\frac{0.145}{4} = 0.03625$

Now, calculate the term inside the parentheses: $1 + 0.03625 = 1.03625$

Step3: Calculate the power

Now, calculate $(1.03625)^{40}$. Using a calculator, $(1.03625)^{40} \approx 4.00957$

Step4: Calculate the amount

Multiply the principal by this value: $A = 8000 \times 4.00957 \approx 32076.56$

Answer:

$$32076.56$