In this activity we consider some typical financial applications that you or your family might encounter.

- Paying for college from savings

- An=(An-1*1.035)-50,000
- After plotting the recursive models I created a table of values.
- I guessed and checked and found that when I plugged in 140,082, that number worked well.

- My parents need to have $190,082.00 before I start college.

- Saving for college

The day you were born, your parents anticipated you going off to college and needing to pay for your tuition. In the previous problem you figured out how much money they will need to have when you start college. Write this amount here: $190,082.00

Then compute the sum of all the deposits they made, including the initial deposit and the recurring deposits. What portion of the target tuition is the sum of all deposits, and what portion is the earned interest?

- An=(1+.025/12)*An-1+500
- After plotting the recursive models I created a table of values.
- I guessed and checked and found that when I plugged in 35,000, that number worked well.

- They needed to deposit 35,000 dollars when I was born. The sum of all the deposits made is $108,000 (57 percent). I did that by doing the intial payment plus 500 times 216. That number is the portion of the total tuition that come from deposits, $82,000 (43 percent) came from earned interest.

- Saving for retirement

What APR does Aunt Sally earn on her account if she plans on living to be 85? What APR would she need if she planned on living to 95? Give your answers accurate to 0.1%.

- An=An-1*(1+x)-20,000
- After plotting the recursive models I created a table of values.
- I guessed and checked and found that when I plugged in .0054 and .035, those numbers worked well.

- If Aunt Sally plans on living to 85, she will need an APR of .54%, and she will run out of money on the very last day. If Aunt Sally plans on living to 95, she will need an APR of 3.5 percent, and she will run out of money on the very last day.

- Paying off a car loan

Compute the sum of the 60 payments that the family made. What portion of the total payment went towards interest, and what portion went towards the purchase price of the car?

- An=An-1*(1+0.06/12)-x
- After plotting the recursive models I created a table of values.
- I guessed and checked and found that when I plugged in 445, that number worked well.

The monthly payment should be $445. The sum of the 60 payments made is 26,700 dollars; I did that by multiplying 445 by 60. 15 percent went towards interest and 85 percent went towards paying for the purchase price of the car.