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

Nicholas retired at the age of 64. He invested £900000 in an annuity fund which returns 6% p.a. compounded monthly. He wants the money to last for 25 years.

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

£ Correct Wrong

Nicholas's sister retired at the age of 57. She invested £700000 in an annuity fund which returns 2.9% p.a. compounded monthly. She withdraws £3500 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

Nicholas's brother deposits $630000 in an annuity fund which earns 4.3% 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 Nicholas's brother's fund after 10 years.

$ Correct Wrong

Professor Collins invested £530000 in an annuity fund which returns 2.2% 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 £87000 is invested with a 2.4% 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
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This is Amortisation and Annuities level 2. You can also try:
Level 1

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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.

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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


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