MATH SOLVE

10 months ago

Q:
# My cousin borrowed $15,000 for a new car loan for 5 years. He told me that at the end of the loan, he had paid $21,000 for the interest and principal. What was the rate of the loan? A. 7% B. 8% C. 9% D. 10%

Accepted Solution

A:

To solve this problem we are going to use the simple interest formula: [tex]A=P(1+rt)[/tex]

where

[tex]A[/tex] is the sum of the interest and the principal

[tex]P[/tex] is the principal

[tex]r[/tex] is the interest rate in decimal form

[tex]t[/tex] is the time in years

We know for our problem that [tex]A=21000[/tex], [tex]P=15000[/tex], and [tex]t=5[/tex]. Now, let [tex]x[/tex] represents our interest rate. To express the interest rate in decimal form, we are going to divide the rate by 100%:

[tex]r= \frac{x}{100} [/tex]

[tex]r=0.01[/tex].

Now that we have all the values we need, lets replace them in our simple interest formula to find the interest rate:

[tex]A=P(1+rt)[/tex]

[tex]21000=15000[1+(0.01x)(5)][/tex]

[tex] \frac{21000}{15000} =1+0.05x[/tex]

[tex]1+0.05x=1.4[/tex]

[tex]0.05x=0.4[/tex]

[tex]x= \frac{0.4}{0.05} [/tex]

[tex]x=8[/tex]

We can conclude that the interest rate of your cousin's loan was 8%.

where

[tex]A[/tex] is the sum of the interest and the principal

[tex]P[/tex] is the principal

[tex]r[/tex] is the interest rate in decimal form

[tex]t[/tex] is the time in years

We know for our problem that [tex]A=21000[/tex], [tex]P=15000[/tex], and [tex]t=5[/tex]. Now, let [tex]x[/tex] represents our interest rate. To express the interest rate in decimal form, we are going to divide the rate by 100%:

[tex]r= \frac{x}{100} [/tex]

[tex]r=0.01[/tex].

Now that we have all the values we need, lets replace them in our simple interest formula to find the interest rate:

[tex]A=P(1+rt)[/tex]

[tex]21000=15000[1+(0.01x)(5)][/tex]

[tex] \frac{21000}{15000} =1+0.05x[/tex]

[tex]1+0.05x=1.4[/tex]

[tex]0.05x=0.4[/tex]

[tex]x= \frac{0.4}{0.05} [/tex]

[tex]x=8[/tex]

We can conclude that the interest rate of your cousin's loan was 8%.