# Math Modelling Project

## Objective

To find the most economically wise loan for a four years engineering university course in National University of Singapore.

## Assumptions

1. Four years Engineering course in National University of Singapore
2. Starting work immediately after graduation
3. Starting pay of \$3000
4. Interest rate remains constant
5. No inflation
6. Course fee: \$7850 per annum

## 1) CPF Education Loan

Course: Engineering

Total Fee =\$31,400

Conditions

1. Repayment will start one year after date of graduation or date of leaving the institution, whichever is earlier
2. Interest starts accruing from the day of withdrawal
3. Interest pegged to the prevailing CPF Ordinary Account interest rate which is currently 2.5% pa
4. Repayment period: a maximum period of 12 years
5. The minimum monthly instalment rate is \$100. Students are encouraged to fully repay the loan within 6 years to reduce the interest incurred for the loan

Calculations

Case 1: Withdraw fees for 4yrs at once

Course fee for 4yrs= 7850(4)=31400

Total Amount to pay: ar^n=31400(1.025)^n

## 2) NUS university loan

Course: Engineering

Tuition Fee per annum: 7850 (With MOE Tuition Grant Scheme, work in SG minimum for 3 years)

Total Fee =\$31,400

Conditions

1. 6 months after graduation or upon securing employment, whichever is earlier.
2. Can pay all at once or installments (>100 monthly) up to 20 years
3. Interest is on average prime rate of DBS OCBC and UOB
4. Determined on the first day of each quarter (Have to assume the interest rate does not change over the course of 4 years)
5. Interest free loan, repayment must be done within 5 years

Calculations

Starting pay: \$3000

Yearly income: \$36,000

Yearly repayment: 31,400/5 = \$6280

Monthly repayment = 6280/12= \$523.33

## 3) Bank Loan

Course: Engineering

Tuition Fee per annum: 7850 (With MOE Tuition Grant Scheme, work in SG minimum for 3 years)

Total Fee =\$31,400

Conditions

1. Interest rate starts right after studies
2. Can pay all at once or installments
3. Interest is on average prime rate of DBS OCBC and UOB ( currently 5%p.a.
4. Up to 20% of the subsidized tuition fees payable by Singapore students and S\$3,600 annual living allowance.
5. Interest-free during course of study.
6. Up to 20 years repayment period for interest bearing loan and up to 5 years for interest free loan with repayment commencing after course completion.
7. Minimum monthly repayment of \$100.

Calculations

Starting pay: \$3000

Yearly income: \$36,000

Yearly repayment: 31,400/5 = \$6280

Monthly repayment = 6280/12= \$523.33

## limitations

1. In reality, there is bound to have inflation.
2. Might not be able to find job immediately