Math help... i'm having trouble solving this problem!?

Question

Okay so Josie is a nine year who recieved an inheritance of $10,000 and put it in her bank account but she wants to spend some when she sixteen. The equation for this problem is 10,000 x 1.075^ and the minimum deposit of the bank is 10,000 but the problem is i need to figure out how much money she can spend when she's sixteen while still being able to have at least $13,000 in her bank account by age 18. So how much money can she spend without going over limits? Can someone please help me answer this question and tell me how to do it?

Answer 1

Let's assume it will be 7 years before Josie turns 16.
Then with yearly compounding when she turns 16 she will have 10000(1.075^7) = $16,590.

Now if she takes out x dollars she will have left16590-x
Then 13000 = (16590-x)(1.075^2)
13000 = (16590 -x)(1.156)
13,000 = 19178 - 1.156x
x= (19178-13000)/1.156 = $5344
So she can take out $5344 at age 16 and still have $13,000 at age 18

Answer 2

the equation means that you multiply the sum you have by 1.075 to the power of how many years it is there. We know that at age 18 she wants to have 13,000 dollars, so if we call the sum at age 16 Y then Yx1.075^2=13,000. This means that Y=approx. 11,250$. This means that as long as there is 13,000$ in her account at age 16, she'll be fine. With the equation, and taking the 7 years til she reaches sixteen, we find that 10,000x1.075^7=approx. 16,590$, meaning she can withdraw 5,340$ at age 16 and still have enough.

Answer 3

@16 she will have 10000*1.075^7=$16590
To have 13000 @18, she had to have in her account $13000/1.075^2=$11249
So, she can spend 16590-11249=5.341