Question

Sarah took out a $30,000 loan at a 4% interest rate to put a new pool in her backyard. If the interest is compounded quarterly, write a function to model this situation. How much interest will she have paid after 12 years?

Answer 1

Answer: $48,366.78

Step-by-step explanation:

3000(1+0.04/4) 4t

Answer 2

The function is A = 30,000(1+0.04/4)^(4t) and the compound interest is $18,366.78 if the interest is compounded quarterly.

What is compound interest?

It is defined as the interest on the principal value or deposit and the interest which is gained on the principal value in the previous year.

We can calculate the compound interest using the below formula:

$\rm A = P(1+\dfrac{r}{n})^{nt}$

Where A = Final amount

          P = Principal amount

          r  = annual rate of interest

          n = how many times interest is compounded per year

          t = How long the money is deposited or borrowed (in years)

Here P = $30,000

r = 4% = 0.04

n = 4

t = 12

The function of this situation:

$\rm A = 30,000(1+\dfrac{0.04}{4})^{4t}$

Plug t = 12 in the above function.

$\rm A = 30,000(1+\dfrac{0.04}{4})^{4\times12}$

A = $48,366.78

So compound interest CI = 48,366.78 - $30,000

CI = $18,366.78

Thus, the function is A = 30,000(1+0.04/4)^(4t) and the compound interest is $18,366.78 if the interest is compounded quarterly.

Learn more about the compound interest here:

brainly.com/question/26457073

#SPJ2