The interest rate on a car has increased 50% over the last 10 years and is now 9%. What was the rate 10 years ago?

Question

Percentages in story problems

Answer 1

The most straightforward method for solving this problem is to write a simple algebraic expression. 

 

First, we are searching for the interest rate 10 years ago: call it X.

 

The interest rate increased 50% over the last 10 years. This means that the total increase was 50%. Recall that percentages can be written in decimal form. So, 50% is the same as .5, and 100% is the same as 1.0. 

 

 

9 percent is the interest rate now, and it can be thought of as 100% of the initial interest rate plus the 50% increase. 

 

Algebraically:

 

1.5X = 9%; this reads 150% of X (1.5X) equals 9%: 150% of X is the same as X increasing by 50%.

X = 9/1.5;divide by 1.5

X = 6

 

So, the initial interest rate was 6 percent. To check the answer, you can calculate 50% of 6 (6 * .5) which is 3. You can then add the value that is 50% of 6% (3%) to 6%and get 9%. 

 

Understand that there is a difference between percent increases and percentage point increases. If my 9% interest rate increased by 50%, then my new interest rate is 9% plus 50% of 9%: 9% + 4.5% = 13.5%. On the other hand, if my 9% interest rate increases by 50 percentage points, this means that the 50% was added to 9%, and my new interest rate is 59%.