Respuesta :
Answer:
The annual interest rate is 6.12%.
Step-by-step explanation:
This is a compound interest problem
The compound interest formula is given by:
[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]
In which A is the amount of money, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit t and t is the time the money is invested or borrowed for.
In this problem, we have that:
To find the interest rate, we first have to find the value of A, that is, the amount paid. The total amound paid was $3568 paid monthly for 33 months, so:
[tex]A = 33*3,568 = 117,744[/tex]
P is the value of the loan, so [tex]P = 100,000[/tex]
r is the interest rate, the value we have to find.
We have to find the annual interest rate, so [tex]n = 1[/tex].
This value was paid in 33 months. However, the unit of t is years. So [tex]t = \frac{33}{12} = 2.75[/tex]
Applying the formula:
[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]
[tex]117,744 = 100,000(1 + r)^{2.75}[/tex]
[tex](1 + r)^{2.75} = 1.17744[/tex]
To find r
[tex]\sqrt[2.75]{(1 + r)^{2.75}} = \sqrt[2.75]{1.17744}[/tex]
[tex]1 + r = 1.0612[/tex]
[tex]r = 0.0612[/tex]
The annual interest rate is 6.12%.
Answer:
The annual interest rate is 6.12%.
Step-by-step explanation:
This is a compound interest problem
The compound interest formula is given by:
In which A is the amount of money, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit t and t is the time the money is invested or borrowed for.
In this problem, we have that:
To find the interest rate, we first have to find the value of A, that is, the amount paid. The total amound paid was $3568 paid monthly for 33 months, so:
P is the value of the loan, so
r is the interest rate, the value we have to find.
We have to find the annual interest rate, so .
This value was paid in 33 months. However, the unit of t is years. So
Applying the formula:
To find r
The annual interest rate is 6.12%.
