NZ Level 6 (NZC) Level 1 (NCEA)
Comparing Loans
Lesson

Loans come with different interest rates, with various methods of calculating the interest and the repayment amounts, and with different durations over which the loans are to be repaid. There may be extra charges that affect the total amount that the borrower will pay back.

When borrowing money, it is wise to make sure that the terms of the loan are clearly understood and that the agreement the borrower enters into is the least expensive one available that meets his or her requirements. However, it is not always easy to compare the loans offered by several lenders because of the variety of different options that are offered.

Finance for cars and other consumer items is often quoted with a fixed rate of simple interest and a repayment schedule of monthly amounts spread over an agreed number of months. There may be extra fees added in and sometimes there is an initial period during which no payment or reduced payments are made. Whatever the details of the arrangement, what really matters is how much in total will be paid to the lender over the whole period of the loan.

If we know how much is to be borrowed initially and how much will be repaid, we can work out an effective simple interest rate for the loan. This will make it possible to compare different loans.

##### Example 3

The table presents the details of three types of home loans.

Loan Interest Rate (p.a.) Legal Fees Application Fee Service Fee (p.a.)
A: Fixed for 5 years, then variable $5.99%$5.99% $\$160$$160 \550$$550 $\$20$$20 B: Variable 5.74%5.74% \100$$100 $\$375$$375 \25$$25
C: Fixed $6.03%$6.03% $\$160$$160 \775$$775 $\$15$$15 1. Which loan option currently has the lowest annual interest rate? A A B B C C A A B B C C 2. Calculate the total fees that loan A will incur in the first year. 3. If Loan C is taken out on a 3030 year term, calculate the total fees incurred over the term of the loan. 4. The table shows the expected change in the variable rate for the next 4 years. Year Rate change 1 +0.3%0.3% 2 -0.18%0.18% 3 -0.04%0.04% 4 +0.32%0.32% In 4 years, by what percentage will the variable rate of Loan B exceed the fixed rate of Loan C? 5. Home loan rates are expected to fluctuate significantly for the next decade, and as the rate changes, loan repayments change accordingly. If Maria wants to know her exact repayments over the 7 year term of her loan, which should she choose? A A B B C C A A B B C C ##### Example 4 Comparison rates allow for potential loan recipients to quickly compare different loans, accounting for interest rates, fees and other charges. Loan Interest Rate Upfront Establishment Fee Service Fee Standard Variable Rate A 5.34%5.34% \350$$350 $\$10$$10 Standard Variable Rate B 5.34%5.34% \250$$250 $\$10$$10 1. Which loan's comparison rate would you expect to be the higher of the two? Standard Variable Rate A A Standard Variable Rate B B Standard Variable Rate A A Standard Variable Rate B B 2. The comparison rates of each of the loans is shown in the table below. Loan Interest Rate (p.a.) Comparison Rate (p.a.) Standard Variable Rate A 5.34%5.34% 5.5%5.5% Standard Variable Rate B 5.34%5.34% 5.53%5.53% What is the difference between the Interest rate and Comparison rate for Variable Rate Loan B? Express your answer as a percentage. ##### Example 5 Luke is aiming to secure a loan worth \400000$$400000 for a new house.

The terms of the loan are such that he will have to make monthly repayments of $\$23002300 for $25$25 years.

1. How much will Luke have to pay on the loan in the first year?

2. Determine the total amount Luke will repay over $25$25 years.

3. Calulate the total interest payment.

4. The annual nominal rate for the loan is $2.9%$2.9%.

Calculate the effective interest rate if interest is compounded monthly. Give your answer as a percentage correct to two decimal places.

5. If interest were compounded fortnightly at a nominal rate of $2.9%$2.9% p.a., instead of monthly, which of the following scenarios would occur?

You would pay more interest over the lifetime of the loan.

A

You would pay less interest over the lifetime of the loan.

B

You would pay more interest over the lifetime of the loan.

A

You would pay less interest over the lifetime of the loan.

B

### Outcomes

#### NA6-3

Apply everyday compounding rates

#### 91026

Apply numeric reasoning in solving problems