# STPM 2017 Term 3 Mathematics (M) Coursework PBS Assignment

STPM Coursework Sample Solution## Question

An entrepreneur is contemplating to purchase a brand new sealing machine winch costs RM90 000. The machine can be purchased through financing packages provided by 3 suppliers. All suppliers require 30% down payment.

1. Suppliers A, B and C offer a financing package that charges 6% annual rate, compounded monthly, quarterly and semi-annually, respectively, for a period of 5 years.

(а) For each package,

(i) calculate the monthly payment.

(ii) prepare a loan amortization schedule showing the principal and interest breakdown.

(iii) explain why the portion of interest declines.

(b) (i) Calculate the total interest paid for each financing package.

(ii) What relationship exists between compounding frequency and the nominal and the total

interest paid?

2. The entrepreneur uses an annual discount rate of 8% for the machine in his investment appraisal.

The annual operating cost of the machine from each supplier is shown in the table below.

Supplier | Annual Operating Cost (RM) | ||||

Year 1 | Year 2 | Year 3 | Year 4 | Year 5 | |

A | 2200 | 2200 | 2200 | 2200 | 2200 |

B | 2000 | 2000 | 2000 | 2500 | 2500 |

C | – | 2500 | 2500 | 3000 | 3000 |

Calculate the present value of the operating cost of the machine from each supplier.

3. Which supplier would you choose? Justify your choice.

### Solution

#### Question 1 (a) (i) Supplier A

#### Question 1 (a) (i) Supplier B

#### Question 1 (a) (i) Supplier C

### Question 1 (a) (iii)

When you make a payment, the amount paid is a combination of an interest charge and principal repayment. Over the life of the financing, the portions of interest to principal will change.

At first, the payment will be primarily interest, with a small amount of principal included. As the loan matures, the principal portion of the payment will increase, and the interest portion will decrease. This is due to the interest charge being calculated off the present outstanding balance of the loan, which decreases as more principal is repaid. The smaller the loan principal, the less interest is charged.

This process of calculating interest based on the remaining balance continues until the loan is paid off. So each month the amount of interest declines and the amount going to paying off the loan increases. After 60 payments, the loan is fully paid off.

### Question 1 (b) (ii)

The total interest paid increases when the compounding frequency is lower.

Nomimal remains at 6%.

### Question 2

Assume that the entrepreneur pay the annual operating cost by end of the year.

### Question 3

Supplier A. The total interest is lesser. Justify yourself.

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