Answer :
Certainly! Let's solve this problem step by step using the simple interest formula.
The simple interest formula is given by:
[tex]\[ I = P \times r \times t \][/tex]
Where:
- [tex]\( I \)[/tex] is the interest
- [tex]\( P \)[/tex] is the principal amount
- [tex]\( r \)[/tex] is the interest rate (in decimal form)
- [tex]\( t \)[/tex] is the time in years
We are given the following values:
- Interest ([tex]\( I \)[/tex]) = [tex]$40 - Interest rate (\( r \)) = 10% = 0.1 (since 10% as a decimal is 0.1) - Time (\( t \)) = 5 years We need to find the principal amount (\( P \)). Rearranging the simple interest formula to solve for \( P \), we get: \[ P = \frac{I}{r \times t} \] Substitute the given values into the equation: \[ P = \frac{40}{0.1 \times 5} \] First, calculate the denominator: \[ 0.1 \times 5 = 0.5 \] Then, divide the interest by the calculated denominator: \[ P = \frac{40}{0.5} \] Finally, calculate the result: \[ P = 80 \] So, the principal amount (\( P \)) that will generate $[/tex]40 in interest at a 10% interest rate over 5 years is [tex]\(\$80\)[/tex].
The simple interest formula is given by:
[tex]\[ I = P \times r \times t \][/tex]
Where:
- [tex]\( I \)[/tex] is the interest
- [tex]\( P \)[/tex] is the principal amount
- [tex]\( r \)[/tex] is the interest rate (in decimal form)
- [tex]\( t \)[/tex] is the time in years
We are given the following values:
- Interest ([tex]\( I \)[/tex]) = [tex]$40 - Interest rate (\( r \)) = 10% = 0.1 (since 10% as a decimal is 0.1) - Time (\( t \)) = 5 years We need to find the principal amount (\( P \)). Rearranging the simple interest formula to solve for \( P \), we get: \[ P = \frac{I}{r \times t} \] Substitute the given values into the equation: \[ P = \frac{40}{0.1 \times 5} \] First, calculate the denominator: \[ 0.1 \times 5 = 0.5 \] Then, divide the interest by the calculated denominator: \[ P = \frac{40}{0.5} \] Finally, calculate the result: \[ P = 80 \] So, the principal amount (\( P \)) that will generate $[/tex]40 in interest at a 10% interest rate over 5 years is [tex]\(\$80\)[/tex].
