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11.2 Loans

In this section, we will talk about reducing-balance loan. Unlike in ‘Investment’ section where simple interest is applied on the loan and the interest payments don’t change over the life of the loan, reducing-balance loan applies interest on the balance of the loan outstanding at the start of each repayment period.

Each of these will be looked at in turn below through examples.

__Calculating amount owing on a loan__

At a basic level, you will be given loan’s principal, interest rate and repayment information and would be required to work out loan balance at a given period.

Following formulas would be helpful for this:

Balance @ t = (Balance @ t – 1) + (Interest @ t) – Repayment for period

Interest @ t = (Balance @ t – 1) × interest rate for period

*Example 1*

Harry borrowed $28,000 to buy a car with interest of 3.99% p.a. and monthly repayments of $515. What is the amount owing after 3 months?

__Looking up loan repayments from table__

This should generally be straight-forward question where a table will be given, and values need to be looked up to do some loan related calculations.

*Example 2*

Following table shows monthly repayment schedule for $1 borrowed on a loan. What is monthly repayment for a 5-year loan of $15,000 with interest rate of 3.5%p.a.?

__Graph of loan__

*Example 3*

The following chart shows loan balance over months. Answer the following questions:

- How much loan is taken?
- How long the loan is borrowed for?
- Between which months half of the loan is paid off?

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You might find the following videos helpful related to this section:

The following is the type of questions you can expect in exam:

Study notes of this section and other resources can be accessed here:

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