Question

the answers need to be shown in a timeline as well as the answer in #5

=Future value*rate/((1+rate)^t-1)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

=Future value*rate/((1+rate)^t-1)

=8000*9%/(1.09^5-1)
=1336.739656

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?

Answer 1

Answer to part 6)

now the annual rate is 9 %

so first we will calculate the monthly rate considering 9 % as annual effective interest rate

let the monthly rate be x% therefore by formula

(1+x %) ^ 12 = (1+0.09)

x = 0.72% or 0.0072

now every month for 5 years means 60 months

therefore t = 60

so by formula

every month the amount kept aside will be

8000 * 0.72% /(1.0072 ^60 - 1)

= 107.07

7) the payment is equal monthly payment for 60 months

so t = 60

the per annum rate is 6% so per month rate is 0.5%

so i = 0.5

the monthly payment will be 8000/Annuity factor

Annuity factor is [(1 - (1+i)^-t]/ i

= 51.72

therefore monthly payment is 8000/51.72

= 154.66

answer 8 )

amount to be saved = $ 300

Frequency - semi-annually for 10 years

t = 20

rate of interest = 8%

rate of interest for half year = 4%

accumulation factor = [ (1+i) ^ t -1 ] / i

= 29.78

therefore amount accumulated after 10 years = 300*29.78 = $8933.42

9) since the amount is saved from today the interest will be earned for 6 months extra compared to Q 8 where the amount is saved after expiry of every 6 months

so amount accumulated is 8933*1.04 = $ 9290

10) amount needed to set aside now

= 1500/1.1 + 2600/(1.1)^2 + 3000/(1.1)^3

= $ 5766.34

11) Loan = $ 100000

monthly payment = 1801.85

Tenure = 60 months

annuity factor = ( 1 - (1+i)^-60)/i

therefore 1801.85 * annuity factor = 100000

solving we get interest rate of 19.5% Per annum