TUTORIAL 10

  

BUSINESS MATHEMATICS

 

MARCH 2003

 

1. Find the value of RM8,000 compounded continuously for 10 years at an interest rate of 5%

 

2. Solve the following problems:

 

a.)    n = 10, i = 6%, R = 1000, F = ?

b.)    F = 2000, i = 4%, n = 30. R = ?

c.)    F = 8000, i = 5%, n = ? R = 200 (Remember to use – nos. in calculator)

d.)    P = 2500, i = 0.25%, n = 60. R = ?

e.)    P = 50,000, i = 0.5%, n = 24, R = ?

 

 

3. A person wants to deposit $6000 each year for 9 years. If interest is earned at a rate of 8% per year, compute the amount to which the deposits will grow at the end of 9 years if interest is compounded:

 

a.)    Annually, with the $6000 deposited at the end of each year

b.)    Semi-annually, with $3000 deposited at the end of every 6 months

c.)    Quarterly, with the $1500 deposited at the end of every quarter

 

4. What is the value of an annuity at the end of 8 years if $200 per month is deposited into an account earning 6% compounded monthly? How much interest is earned?

 

5. Find the monthly payments necessary to repay a 5-year car loan of $20,000 if interest is computed at 8.5% compounded monthly. Calculate the interest paid over the 5 years

 

6. Parents have set up a sinking fund in order to have RM50,000 in 15 years for their children’s college education. How much is paid semi-annually into an account paying 10% compounded semi-annually?

 

 

7. Parents of a teenage girl want to deposit a sum of money which will earn interest at the rate of 7% compounded semi-annually. The deposit will be used to generate a series if six semiannual payments of $3000 beginning 6 months after the deposit. These payments will help finance the daughter’s college education. What amount must be deposited to achieve this goal? How much interest will be earned on this deposit?

 

8. How much should you deposit in an account paying 10% compounded monthly in order to receive $500 per month for the next 4 years?

 

9. If $500 is deposited in an account each month for 25 years and the account earns 6% compounded monthly, how much will be in the account after the last deposit is made?

 

10. What amount should be deposited in at the end of each month in a sinking fund earning 4% compounded monthly if the amount in the fund after 6 years is to be $120,000?

 

11. A person wishes to have $500,000 in an account for retirement 20 years from now. How much should be deposited quarterly in an account paying 6% compounded quarterly?

 

12. A small-scale business person decides to deposit RM8500 at the end of every year in an account that pays 5% interest, compounded annually. In 20 years, how much will the account amount to?

 

13. Construct the amortization schedule for a $2000 debt that is to be amortized in 4 equal quarterly payments at 2% interest, compounded quarterly.

 

14. The price of a new car is $18,000. Assume an individual makes a down payment of 15% toward the purchase of the car and secures financing for the balance at a rate of 10% per year compounded monthly.

 

a.)    What monthly payment will she be required to make if the car is financed over 36 months? 48 months?

 

b.)    What will the interest charges amount to if she chooses the 36 month plan? The 48-month plan?