Transum Software

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 2: Annuities. Give answers which are amounts of money correct to two decimal places.

Jessica retired at the age of 60. She invested £600000 in an annuity fund which returns 6% p.a. compounded monthly. She wants the money to last for 30 years.

1. Calculate how much she can afford to withdraw each month.

£ Correct Wrong

Jessica's sister retired at the age of 63. She invested £800000 in an annuity fund which returns 1.2% p.a. compounded monthly. She withdraws £4000 each month for living expenses and holidays.

2. Calculate how long it will take for the money to run out. Round you answer down to a whole number of years.

Correct Wrong

Jessica's brother deposits $830000 in an annuity fund which earns 2.9% p.a. interest compounded quarterly. He wants the money to last for 30 years.

3. How much can he afford to withdraw each quarter?

$ Correct Wrong

4. Find the outstanding balance of Jessica's brother's fund after 10 years.

$ Correct Wrong

Professor Collins invested £520000 in an annuity fund which returns 1.6% p.a. compounded monthly. He withdraws £3000 each month.

5. Calculate how long it will take for the money to run out. Round you answer down to a whole number of years.

Correct Wrong

6. How many more months would his money last if he only withdrew £2500 each month? Round you answer down to a whole number of months.

Correct Wrong

7. If £66000 is invested with a 1.7% p.a. interest rate (compounded annually). What is the maximum I can take out of this account at the end of each year if it is to be a perpetuity (a special type of annuity in which the regular payments continue indefinitely)?

£ Correct Wrong

8. What amount must be initially invested into an annuity account if it is to yield £2000 per month for 20 years at a 2% p.a. rate of interest componded monthly?

£ Correct Wrong

Dr Jane Dose retires at age 63 with €75000 in her savings fund. She rolls this money into an annuity fund earning 3.5% p.a. interest compounded monthly.

9. How much will she be able to withdraw each month if her money is to last until her 85th birthday?

Correct Wrong

10. How much more will Dr Dose be able to withdraw each month if her money was to only last one decade?

Correct Wrong

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


Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help.

When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file.

Why am I learning this?

Mathematicians are not the people who find Maths easy; they are the people who enjoy how mystifying, puzzling and hard it is. Are you a mathematician?

Comment recorded on the 7 December 'Starter of the Day' page by Cathryn Aldridge, Pells Primary:

"I use Starter of the Day as a registration and warm-up activity for my Year 6 class. The range of questioning provided is excellent as are some of the images.
I rate this site as a 5!"

Comment recorded on the 1 May 'Starter of the Day' page by Phil Anthony, Head of Maths, Stourport High School:

"What a brilliant website. We have just started to use the 'starter-of-the-day' in our yr9 lessons to try them out before we change from a high school to a secondary school in September. This is one of the best resources on-line we have found. The kids and staff love it. Well done an thank you very much for making my maths lessons more interesting and fun."

Each month a newsletter is published containing details of the new additions to the Transum website and a new puzzle of the month.

The newsletter is then duplicated as a podcast which is available on the major delivery networks. You can listen to the podcast while you are commuting, exercising or relaxing.

Transum breaking news is available on Twitter @Transum and if that's not enough there is also a Transum Facebook page.

Featured Activity



Interactive, randomly-generated, number-based logic puzzle based on the Latin square designed to develop numeracy skills. These puzzles are drag and drop and can earn you a Transum Trophy.


There are answers to this exercise but they are available in this space to teachers, tutors and parents who have logged in to their Transum subscription on this computer.

A Transum subscription unlocks the answers to the online exercises, quizzes and puzzles. It also provides the teacher with access to quality external links on each of the Transum Topic pages and the facility to add to the collection themselves.

Subscribers can manage class lists, lesson plans and assessment data in the Class Admin application and have access to reports of the Transum Trophies earned by class members.

If you would like to enjoy ad-free access to the thousands of Transum resources, receive our monthly newsletter, unlock the printable worksheets and see our Maths Lesson Finishers then sign up for a subscription now:


Go Maths

Learning and understanding Mathematics, at every level, requires learner engagement. Mathematics is not a spectator sport. Sometimes traditional teaching fails to actively involve students. One way to address the problem is through the use of interactive activities and this web site provides many of those. The Go Maths page is an alphabetical list of free activities designed for students in Secondary/High school.

Maths Map

Are you looking for something specific? An exercise to supplement the topic you are studying at school at the moment perhaps. Navigate using our Maths Map to find exercises, puzzles and Maths lesson starters grouped by topic.


If you found this activity useful don't forget to record it in your scheme of work or learning management system. The short URL, ready to be copied and pasted, is as follows:

Alternatively, if you use Google Classroom, all you have to do is click on the green icon below in order to add this activity to one of your classes.

It may be worth remembering that if should go offline for whatever reason, there is a mirror site at that contains most of the resources that are available here on

When planning to use technology in your lesson always have a plan B!

Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.


©1997-2024 WWW.TRANSUM.ORG

© Transum Mathematics 1997-2024
Scan the QR code below to visit the online version of this activity.

This is a QR Code

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.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

Log in Sign up

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

Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly. You can double-click the 'Check' button to make it float at the bottom of your screen.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

Log in Sign up