How Do You Use the Formula for Simple Interest?

Summary

I, p, r, and t are variables in the formula for simple interest
I represents the interest earned
p represents the amount of money originally invested
r represents the interest rate
t represents time in years
I, the amount of interest, is 243
p is what we're solving for, the amount invested
r, the interest rate, is 9%, which is 0.09 as a decimal
t, time, is 18 months, which is 1.5 years
Plug the values into the formula and solve for p

Notes

1. The formula for simple interest states that interest is equal to the amount of money invested times the interest rate times time
2. We can use this formula to figure out how much money Denzel invested
1. I is the amount of interest
2. p is the amount of money invested
3. r is the interest rate
4. t is time in years
1. The formula for simple interest is I=prt
2. I, p, r, and t are the variables in the formula
1. I is a variable that represents interest earned
1. I is a variable that represents interest earned
2. I=243
1. p is a variable that represents the amount of money invested
1. This is our unknown value
2. So we will need to use our formula to solve for p
1. r is a variable that represents the rate of interest
1. r is a variable that represents the rate of interest
2. Our problem gives us an interest rate of 9%
1. When we are working with formulas, we can't use percents as percents
2. But we can convert any percent to a decimal, which we CAN use
1. To convert a percent to a decimal, take the number of the percent and move the decimal two places to the left
2. Since 9 is a whole number, its decimal comes right after the number
3. So moving the decimal two places to the left gives us 0.09
4. This is a value we can use for r, the interest rate
1. t is a variable that represents time in years
1. t is a variable that represents time in years
2. Notice that our problem gives time in months
3. Since the formula needs time in years, we'll have to convert 18 months to years
1. t is a variable that represents time in years
2. Notice that our problem gives time in months
3. Since the formula needs time in years, we'll have to convert 18 months to years
1. t is a variable that represents time in years
2. Divide 18 months by 12 months in a year to get 1.5 years
3. So we can use 1.5 for t
1. I, the interest earned, is 243
2. p, the amount Denzel invested, is our unknown
3. r, the interest rate (as a decimal), is 0.09
4. t, time (in years), is 1.5
1. Now we simplify and solve for p, the amount of money invested
2. We can simplify the right hand side by multiplying 0.09 by 1.5
3. So we get 0.135 times p on the right
1. p is the variable we're solving for, the amount of money invested
1. p is the variable we're solving for, the amount of money invested
1. Division is the opposite of multiplication
2. So to undo the multiplication and get p by itself, we need to divide both sides by 0.135
1. p, our unknown, is now by itself on the right hand side
2. We found the left hand side to be 1800, so this is equal to p
3. So we have solved for p, the amount of money invested: p=1800

Denzel opened a savings account that made 9% annual interest. After 18 months, she had made $243 in interest. How much money did she put into her savings account?

Summary

Notes