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Kenneth loaned $1,200 to his niece to buy a computer. Two years later, she paid him back the $1,200 along with an interest of $96. If the interest that was collected was simple interest, what was the annual interest rate?

Answer :

roundadworthy

Answer:

The  annual interest rate was 4%

Step-by-step explanation:

1. Let's review the data given to us for solving the question:

Loan to Kenneth's niece to buy a computer = US$ 1,200

Duration of the loan = 2 years

Niece paid back to Kenneth = US$ 1,296

Annual interest rate = x%

2. Let's find the annual interest rate after 2 years, using the following formula:

FV = PV * (1 + x)

PV = Loan to Kenneth's niece to buy a computer = US$ 1,200

FV = Niece paid back to Kenneth = US$ 1,296

rate (r) = x

Replacing with the real values:

1,296 = 1,200 * (1 + x)

1.296/1.200 = (1 + x) (Dividing by 1,200 at both sides)

1.08 = 1 + x

1.08 - 1 = x (Subtracting 1 at both sides)

0.08 = x

This is the interest rate for two years, for finding the annual interest rate we divide it by 2, this way:

0.08 / 2 = 0.04 * 100 = 4%

Using the relationship of the simple interest, rate, time, and principal. Then the rate is 4%.

What is simple interest?

Simple interest is the concept that is used in many companies such as banking, finance, automobile, and so on.

Given

Kenneth loaned $1,200 to his niece to buy a computer.

Two years later, she paid him back the $1,200 along with an interest of $96. Then the amount will be $1,296.

We know the formula for simple interest (S.I.)

[tex]\rm S.I. = \dfrac{PRT}{100}\\[/tex]

Where

R (rate)

P (principal) = $1,200

T (time) = 2

Then the rate will be

[tex]\begin{aligned} 96 &= \rm \dfrac{1200* 2 *R}{100}\\\\9600 &= \rm 2400*R\\\\\rm R &= \dfrac{9600}{2400}\\\\\rm R &= 4 \ \% \end{aligned}[/tex]

Thus, the rate is 4%.

More about the simple interest link is given below.

https://brainly.com/question/9895511

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