Mr. Johnson borrowed $8000 for 4 years to make home improvements. If he repaid a total of $10,320, at what interest rate did he borrow the money?

Respuesta :

MsRay

Answer:

7.25%

Step-by-step explanation:

Simple interest can be found using the following formula:

I = prt, where I = the interest, p = principal amount, r = interest rate and t = time

In this problem, you are solving for 'r', so you can plug in the other values and use inverse operations to find the rate.  

Since Mr. Johnson repaid $10,320 on an $8000 loan, his total interest paid was $10,320 - $8,000 = $2,320.

2320 = 8000(4)r

2320 = 32000r

Divide by 32000 on both sides: 2320/32000 = 32000r/32000

r = 0.0725

multiply by 100 for percentage:  0.0725 x 100 = 7.25%

At a 7% interest rate did he borrow the money.

Given that,

Mr. Johnson borrowed $8000 for 4 years to make home improvements.

If he repaid a total of $10,320.

We have to determine,

At what interest rate did he borrow the money?

According to the question,

The total amount he borrowed = $8000

Time period = 4 years

Repaid amount = $10,320

Left amount = Repaid amount - borrowed amount

Left amount = 10,320 - 8000

Left amount = 2320

Therefore,

The interest rate did he borrow the money is given by the following formula;

[tex]\rmLeft \ amount= Principal \times Rate \times Time\\\\2320 = 8000 \times 4 \times Rate\\\\Rate = \dfrac{2320}{32000}\\\\Rate = 0.07[/tex]

Converting into a percentage by multiply by 100,

[tex]\rm Rate = 0.07\times 100\\\\Rate = 7 \ percent[/tex]

Hence, At a 7% interest rate did he borrow the money.

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