In this activity we consider some typical financial applications that you or your family might encounter.
  1. Paying for college from savings​
Your parents are going to pay for four years of college by making annual payments of $50,000 from their savings account that earns 3.5% APR, compounded annually. The payments are made at the beginning of each academic year, for four consecutive years. Your parents’ goal is to have sufficient funds in their account to pay for all four years, and to have a zero balance after the fourth payment. How much money do your parents need to have in their savings account just before you start college? Approximate the answer accurate to $500.
  1. An=(An-1*1.035)-50,000
  2. After plotting the recursive models I created a table of values.
  3. I guessed and checked and found that when I plugged in 140,082, that number worked well.
  1. My parents need to have $190,082.00 before I start college.
  1. 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
Your parents started saving by opening an account with an initial deposit, and made monthly deposits of $500. The account earned 2.5% APR compounded monthly. If, after 18 years (216 months), they met the target amount, how much money did they need to deposit in the account when you were born? Give your answer accurate to $500.
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?
  1. An=(1+.025/12)*An-1+500
  2. After plotting the recursive models I created a table of values.
  3. I guessed and checked and found that when I plugged in 35,000, that number worked well.
  1. 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.
  1. Saving for retirement
Aunt Sally just turned 65 and she is about to retire. She is convinced that she will have enough money to last the rest of her life. She has $360,000 in her savings account that receives a fixed APR, compounded annually. For her living expenses, she needs $20,000 every year to supplement her Social Security income.
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%.
  1. An=An-1*(1+x)-20,000
  2. After plotting the recursive models I created a table of values.
  3. I guessed and checked and found that when I plugged in .0054 and .035, those numbers worked well.
  1. 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.
  1. Paying off a car loan
A family wishes to take out a loan to buy a car. The total loan amount is $22,695, and the interest rate is 6% APR, compounded monthly. The loan needs to be payed off in 60 months. What should be the monthly payment? Give your answer accurate to $1.
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?
  1. An=An-1*(1+0.06/12)-x
  2. After plotting the recursive models I created a table of values.
  3. 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.