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Math  /  Algebra

QuestionFeng invests money in an account paying simple interest. He invests $70\$ 70 and no money is added or removed from the investment. After one year, he has $70.70\$ 70.70. What is the simple percent interest per year?
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Studdy Solution

STEP 1

1. Feng invests \$70 in an account.
2. The account pays simple interest.
3. No additional money is added or removed from the investment.
4. After one year, the total amount is \$70.70.
5. We need to find the simple interest rate per year in percentage.

STEP 2

1. Identify the formula for simple interest.
2. Calculate the interest earned.
3. Use the simple interest formula to find the interest rate.
4. Convert the interest rate to a percentage.

STEP 3

Identify the formula for simple interest. The formula for simple interest is:
I=P×r×t I = P \times r \times t
where I I is the interest earned, P P is the principal amount, r r is the interest rate, and t t is the time in years.

STEP 4

Calculate the interest earned. The total amount after one year is \$70.70, and the principal amount is \$70. Therefore, the interest earned is:
I=70.70−70=0.70 I = 70.70 - 70 = 0.70

STEP 5

Use the simple interest formula to find the interest rate. We know I=0.70 I = 0.70 , P=70 P = 70 , and t=1 t = 1 . Substitute these values into the formula:
0.70=70×r×1 0.70 = 70 \times r \times 1
Simplify to find r r :
r=0.7070 r = \frac{0.70}{70}

STEP 6

Calculate r r :
r=0.7070=0.01 r = \frac{0.70}{70} = 0.01

STEP 7

Convert the interest rate to a percentage. Multiply the decimal interest rate by 100 to convert it to a percentage:
Interest Rate=0.01×100=1% \text{Interest Rate} = 0.01 \times 100 = 1\%
The simple percent interest per year is:
1% \boxed{1} \%

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