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Amortisation and Annuities

Exercises containing problems about gradually paying off loans and calculating pension plans.

Interest Amortisation Annuities Exam-Style Description Help More Finance

This is level 1: Amortisation. Give answers which are amounts of money correct to two decimal places.

Lily takes out a loan for £16000 at 6% nominal APR compounded monthly. She makes monthly payments for 7 years.

1. Calculate the amount of the monthly payments.

£ Correct Wrong

2. Calculate the total amount Lily will have paid back altogether by the end of the 7 years.

£ Correct Wrong

A student takes out a loan for £12000 at 7% nominal APR compounded quarterly. The repayments are to be made every three months for 9 years.

3. Calculate the amount of the quarterly payments.

£ Correct Wrong

4. What is the total amount of interest this student will pay?

£ Correct Wrong



Less than £213 pm
Initial deposit of only £5000 then easy monthly repayments over 5 years. Terms and conditions apply.

A car is advertised on sale for £16000. A big orange sign in the car's windscreen advertises a tempting way to pay for the car. In the small print it can be seen that the deal involves a £5000 deposit followed by monthly payments of £212.66 for 5 years.

5. What is the rate of interest (nominal APR) being charged to the customer in this scheme? Give your answer to the nearest whole number.

% Correct Wrong

6. What is full cost of the car if purchased using the terms of this scheme?

£ Correct Wrong

Another scheme to purchase this same car is no deposit but 4 annual payments based on a 5% nominal APR compounded annually.

7. What would the annual payments be?

£ Correct Wrong

8. What is full cost of the car if purchased using the terms of this second scheme?

£ Correct Wrong

Lily's mother takes out a loan for £1100 for emergency house repairs. She will repay the loan with a payment each month at 2.6% nominal APR compounded monthly spread over the course of a year.

9. Calculate the amount of the monthly payments.

£ Correct Wrong

10. What is the outstanding balance on the loan after 6 months? Give this answer to the nearest pound.

£ Correct Wrong

This is Amortisation and Annuities level 1. You can also try:
Level 2


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Description of Levels



Interest - Exercises on compound interest on investments and loans.

Level 1 - Amortisation

Level 2 - Annuities

Exam Style Questions - A collection of problems in the style of GCSE or IB/A-level exam paper questions (worked solutions are available for Transum subscribers).

More Financial Maths including lesson Starters, visual aids, investigations and self-marking exercises.

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Curriculum Reference

See the National Curriculum page for links to related online activities and resources.


These exercises are designed for those who have access to a graphic display calculator (GDC) with a Finance Solver function. It is possible to answer the questions using only a scientific calculator but not easy.

A great way to answer the questions in these exercises without a GDC is by creating a table of interest, payment and balance in a spreeadsheet.

Amortisation Spreadsheet Example


Amortization is is paying off an amount owed over time by making planned, incremental payments of principal and interest. In accounting, amortisation refers to writing off an asset's cost as an expense over its estimated useful life to reduce a company's taxable income.

The word amortise (which can also be spelled amortize) comes from the latin ad mortem meaning 'to death'

The formula to find the payments for amortisation is:

$$ Pmt = PV \times \frac{r(1+r)^n}{(1+r)^n -1} $$

It is recommended to use the Finance Solve on your GDC for this topic. [See TI-Nspire Essentials].

menu ⇒ Finance ⇒ Finance Solver

These are the variables used in the Finance Solver function:

There is also a function on the GDC that can produce a table showing all the datails of the gradual loan repayment:

menu ⇒ Finance ⇒ Amortisation ⇒ Amortisation Table

These are the variables used in the Amortisation Table function:

The values should be typed into the function in this order:



An annuity is the investment of a lump-sum which provides the fund from which regular withdrawals are made over a fixed time period. The investment earns interest according to the balance of the annuity each time period. The payments may be made weekly, monthly, quarterly, yearly, or at any other regular interval of time.

An annuity which provides for payments for the remainder of a person's lifetime is a life annuity.

It is recommended to use a GDC for your working. See TI-Nspire Essentials for an example of how to use the Finance Solver. Note that PV (present value, the amount of the lump-sum) should be negative and the payments (PMT) should be positive.

The formula for calculating the payments from an annuity is the same as that for an amortisation

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