In this video we discuss how to solve for time in simple interest problems. We go through the formula for solving for time in simple interest problems and go through a few examples.
Transcript/notes
The formula for calculating simple interest is interest equals, the principal, times the rate, times the time frame, which can be written as I equals p, times r, times t, or I equals prt.
If we want to solve for time, we can modify this equation by dividing both sides by principal times rate, P times R, and we get the formula time equals, interest divided by principal times rate.
As an example, lets say that someone borrowed $1500 and paid $288 in interest. The simple interest rate was 6.4%, how many years was the loan for?
Using our formula of time equals, interest divided by principal times rate, the principal or initial amount borrowed was $1500, the interest paid is $288, the rate is 6.4%, which we must convert to a decimal, and to do that, we move the decimal 2 places to the left to get .064. So, we have time equals, $288 divided by $1500 times .064. $1500 times .064 equals $96, and $288 divided by $96 equals 3, and the dollar signs cancel out. So, the loan was for a time period of 3 years.
The previous example nicely turned out to be 3 years, but this isn’t always the case. For instance, using the last example, what if the interest paid was $240? In that case we would have $240 in the numerator, and would get an answer of 2.5 years, or you could say 30 months.
And, many times we need the time in days or months. Since the formula gives us a result tor time in years, to convert it to time in days, we would multiply the result by 365, and for time in months, we would multiply the result by 12.
As an example, lets say that Tom deposits $9000 in an account paying 6% simple interest and earns $320 in interest. How many days did the deposit earn interest? And how many months did the deposit earn interest?
Using the formula, the principal was $9000, the interest paid is $320, and the rate is 6%, which we must convert to a decimal, and to do that, we move the decimal 2 places to the left to get .06. So, we have time equals, $320 divided by $9000 times .06. $9000 times .06 equals $540, and $320 divided by $540 equals .593 rounded off, and the dollar signs cancel out. To convert time to days, we multiply our answer of .593 times 365, which equals 216 days rounded off. So, the money was on deposit for 216 days.
Next, to convert time to months, we multiply our answer of .593 times 12, which equals 7.12 months.
And here are a couple more examples on the screen for you of how to solve for time in simple interest problems.
Timestamps
0:00 Formula for calculating simple interest
0:12 Formula to solve for time in simple interest problems
0:24 Example problem solving for time
1:38 How to solve for time in days and months
1:49 Example solving for time in days and months
3:00 More example problems solving for time
