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

Olivia takes out a loan for £14000 at 6% nominal APR compounded monthly. She makes monthly payments for 6 years.

1. Calculate the amount of the monthly payments.

£ Correct Wrong

2. Calculate the total amount Olivia will have paid back altogether by the end of the 6 years.

£ Correct Wrong

A student takes out a loan for £14000 at 7% nominal APR compounded quarterly. The repayments are to be made every three months for 8 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

Windscreen

SALE

Less than £178 pm
Initial deposit of only £5000 then easy monthly repayments over 8 years. Terms and conditions apply.

A car is advertised on sale for £19000. 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 £177.24 for 8 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 7 annual payments based on a 4% 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

Olivia'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
Check

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

Instructions

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.

Transum.org

This web site contains over a thousand free mathematical activities for teachers and pupils. Click here to go to the main page which links to all of the resources available.

Please contact me if you have any suggestions or questions.

Email address

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 10 April 'Starter of the Day' page by Mike Sendrove, Salt Grammar School, UK.:

"A really useful set of resources - thanks. Is the collection available on CD? Are solutions available?"

Comment recorded on the 18 September 'Starter of the Day' page by Mrs. Peacock, Downe House School and Kennet School:

"My year 8's absolutely loved the "Separated Twins" starter. I set it as an optional piece of work for my year 11's over a weekend and one girl came up with 3 independant solutions."

Teacher! Are you delivering Maths lessons online?

Tutors! Are your tutorials now taking place via a video link?

Parents! Has home-schooling been thrust upon you at short notice?

There are many resources to help you on the Maths At Home page. From ready made lesson plans to software suggestions and it's all free.

Stay safe and wash yout hands!

Featured Activity

Shunting Puzzles

Shunting Puzzles

These puzzles are Transum's versions of the shunting or switching puzzles made popular by train enthusiasts and logic puzzle solvers.

Answers

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:

Subscribe

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.

Teachers

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:

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.

Apple

©1997-2020 WWW.TRANSUM.ORG

© Transum Mathematics 1997-2020
Scan the QR code below to visit the online version of this activity.

This is a QR Code

Transum.org/go/?Num=853

Description of Levels

Close

Close

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.

Help

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

Amortisation

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:

amortTbl(NPmt,N,I,PV,Pmt,FV,PpY,CpY)

Annuity

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

Close

Close