A Composite interest question? (9th grade level)

Question

Q: A school increases its intake by 10% each year. If it starts with 1000 students, how many will it have at the beginning of the fourth year of expansion?

The answer from the answer sheet is 1331 students.....but I don't get why it is this answer.
I use the formula: A=P(1+r%)^t
But A= 1000*(1+10%)^4 equals to 1464.1. Even if I subtract the principle P, it is still 464.1. And this is not the answer!

I wonder if my method is wrong. Please help! Thanks!

Answer 1

Hi Lydie, 

 

This stumped me at first too. I think the problem is with raising it to the fourth power. It's asking for the beginning of the fourth year--before you get the new students for that year. 

 

Think of it like this. 

 

Right now, in year 1, you have 1000 students. 

By the beginning of year 2, you have 1100 students. (This is 1000 + (0.1 *1000) or the 1000 plus the increase in 10%)

By the beginning of year 3, you have 1210 students. (1100 + (0.1*1100))

By the beginning of year 4, you have 1331 students (1210 + (0.1*1210))

 

This should be the same as if you use the formula, but with t=3. 

 

This might seem a little strange, but I think the trick here is looking for how many times the 10% increase is happening. If we want the number of students at start of year four, we are not considering the fourth year's increase yet. It's the same as at the end of year 3, so t=3. 

 

Hope that helps!