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Math  /  Algebra

QuestionA man needed money for college. He borrowed $5,000\$ 5,000 at 16%16 \% simple interest per year. If he paid $200\$ 200 interest, what was the duration of the loan?
The duration of the loan is □\square year. (Round to two decimal places as needed.)

Studdy Solution

STEP 1

1. The principal amount borrowed is 5,000.<br/>2.Theannualsimpleinterestrateis165,000.<br />2. The annual simple interest rate is 16%.<br />3. The total interest paid is 200.
4. We need to find the duration of the loan in years.

STEP 2

1. Understand the formula for simple interest.
2. Define the known values and the unknown variable.
3. Set up the equation using the simple interest formula.
4. Solve for the duration of the loan.

STEP 3

Understand the formula for simple interest.
The formula for simple interest is given by: I=P×r×t I = P \times r \times t
where: - I I is the interest, - P P is the principal amount, - r r is the rate of interest per year (as a decimal), - t t is the time in years.

STEP 4

Define the known values and the unknown variable.
Given: - I=200 I = 200 - P=5000 P = 5000 - r=16%=0.16 r = 16\% = 0.16
Unknown: - t t (the duration of the loan in years)

STEP 5

Set up the equation using the simple interest formula.
Substitute the known values into the simple interest formula: 200=5000×0.16×t 200 = 5000 \times 0.16 \times t

STEP 6

Solve for the duration of the loan.
First, simplify the equation: 200=800×t 200 = 800 \times t
Now, solve for t t by dividing both sides by 800: t=200800 t = \frac{200}{800}
Simplify the fraction: t=0.25 t = 0.25
The duration of the loan is: 0.25 \boxed{0.25}

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