Question

These are TVM problems

Homework Problems:

1. Aaron is planning a dream vacation traveling for 4 years through each of the countries in Central and South America. He will need $36,000/each year to meet expenses. How much money must he have at the start of his trip to be able to fund his dream? Assume the money will earn 4%.

2. Billy wants to have $25,000 available for a down payment in 10 years. He just received an inheritance and wants to know how much he would have to set aside now in order to reach his goal if his money were to earn 7%?

3. Refer to #2, instead of 7%, the rate is 18%. What would your answer be?

4. Based on your answers from #2 and #3, complete this sentence: The higher the interest rate, the ________________ the present value.  WHY is this true?? Write your answer to this question BELOW your answer to this question.

Your answer is important to remember – it shows a key relationship and comes up in later chapters (obviously, no timeline for this problem[KG1] )

5. You want to buy a boat in 5 years and need to have $8,000 available to use as a down payment. How much would you need to save each year to reach that goal and your money will earn 9%? h

6. Refer to #5. Instead of saving each year, you want to save each month to reach your desired $8,000. Assume the same rate and term as above. Note: you cannot divide your answer to #5 by 12.

7. Sandy is buying a car and wants to get a loan of $8,000. If the rate is 6% and term is 5 years, what would the monthly payments be?

8. Diane is going to save $300 every 6 months (twice a year) for 10 years. If the rate is 8%, how much will she have?

9. Ken is going to save $300/month for 10 years, but will start TODAY. If the rate is 8%, how much will he have?   Note the difference in your answer to this problem from #8. Explain WHY is there a difference in your answers?

10. Uncle Guido wants to give you a gift. He tells you he will write a check to you of $1500 in 1 year, $2,600 in year 2 and $3,000 in year 3.   How much does Guido have to set aside now in order to have sufficient funds to write all of those checks? Assume a 10% rate.

11. You get a loan of $100,000 for 10 year term. If the payments are $1,801.85/month, what is the interest rate on this loan (remember all rates are always quoted as annual figures)? Hint: set up timeline and determine which type of TVM problem it resembles. Then solve.

12. Carla will give $200 to you every three months for 10 years (4x per year). At year 10 she will also give $10,000 to you. What amount of money must be available in her bank account in order for her to have enough money to meet her promise. The rate is 12%. Hint: this problem is a combination of 2 types of TVM problems. Your final answer is the sum of the two.

13. Brett has contract that will pay him $10,000 at the end of 5 years. Brett wants money now and not in 5 years, so he is willing to have contract signed over to you (so you would receive that money) if you give him some money today. If you require a 12% interest rate on money you lend to friends. What is the maximum amount you would you be willing to pay for this contract?

[KG1]This is not useful here. Do another problem or omit.

Answer 1

Aaron is planning a dream vacation traveling for 4 years through each of the countries in Central and South America. He will need $36,000/each year to meet expenses. How much money must he have at the start of his trip to be able to fund his dream? Assume the money will earn 4%.
=Amount/rate*(1-1/(1+rate)^t)
=36000/4%*(1-1/1.04^4)
=130676.2281

Billy wants to have $25,000 available for a down payment in 10 years. He just received an inheritance and wants to know how much he would have to set aside now in order to reach his goal if his money were to earn 7%?
=Future Value/(1+rate)^t
=25000/1.07^10
=12708.7323

Refer to #2, instead of 7%, the rate is 18%. What would your answer be?
=25000/1.18^10
=4776.611673

Based on your answers from #2 and #3, complete this sentence:
The higher the interest rate, the lowerthe present value.

WHY is this true??
It is true because one will earn higher interest on amount depsoited thus lesser value is required now to accumulate a given sum

You want to buy a boat in 5 years and need to have $8,000 available to use as a down payment. How much would you need to save each year to reach that goal and your money will earn 9%?
=Future value*rate/((1+rate)^t-1)
=8000*9%/(1.09^5-1)
=1336.739656