1.4 & 1.7 Compound Interest, Loans and Annuities

This chapter explores the financial application of geometric sequences in the form of compound interest calculations. It then goes on to look at loans and annuities where payments at regular intervals make for some complex algorithms. The finance app on your GDC is a huge help here and this chapter will talk you through using all of that.

Key Concepts

In this chapter you will learn about and practice,

The concept of compound interest as repeated percentage increase and depreciation as repeated percentage decrease.
working with different compounding periods
Solving problems in involving loans and annuities
Learning how to use your GDC in different ways and, in particular the finance app to solve problems in involving all of the above

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Essentials

Compound Interest Slides

The following slides outline the key points to know and understand about compound interest and include lots of worked examples. See the video section below for explanations.

Compound Interest Videos

The following series of videos explain all the key points and go through worked examples

1. Compound Interest Concept

Here we look at understanding and carrying out compound interest calculations, how it works and what it means.

2. Different Compounding periods

In this video we look at how to deal with different compounding periods, when interest is calculate more often than once a year.

3. The Compound Interest Formula

Here we look at the compound interest formula that you have in your formula booklets and show how it fits with what was done in the first two videos.

4. The finance app for Compound Interest calculations

Here we look at how to use your finance app to do compound interest calculations and, in particular, for problems where you need to solve for time and interest rate.

5. Depreciation

This video shows how the same principles used above apply to work with depreciation.

Loans & Annuities Slides

The following slides outline the key points to know and understand about loans and annuities and include lots of worked examples. See the video section below for explanations.

Loans & Annuities Videos

The following series of videos explain all the key points and go through worked examples

6. Introduction to Loans & Annuities

Here we look at understanding and carrying out compound interest calculations, how it works and what it means.

7. Focus on loans

Working through examples of solving problems with loans.

8. Focus on savings annuities

Working through examples of solving problems with savings annuities.

9. Focus on gift annuities

Working through examples of solving problems with gift annuities.

....

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Summary - coming soon

These slides summarise the essential understanding and skills in this topic. They are what we have previously included as 'Flash Cards' or 'revision cards

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Test yourself

Self Checking Quiz

Practice your understanding on these quiz questions. Check your answers when you are done and read the worked solutions when you get stuck. If you find there are still some gaps in your understanding then go back to the videos above.

You invest $4000 in an account that pays compound interest at 5% for 6 years. Work out the value of your investment after 6 years if interest is compounded...

a) Annually

b) Monthly

c) Quarterly

Give your answers to the nearest dollar.

a) $

b) $

c) $

Use the compound interest formula

$4000\times\left(1+\frac{5}{\frac{k}{100}}\right)^{\left(6\times k\right)}$

a) k = 1, b) k = 12, c) k = 4

You invest $42300 in an account that pays compound interest at 2.5% for 10 years. Work out the value of your investment after 10 years if interest is compounded...

a) Semi Annually

b) Monthly

c) Quarterly

Give your answers to the nearest dollar.

a) $

b) $

c) $

Use the compound interest formula

$42300\times\left(1+\frac{6}{\frac{k}{100}}\right)^{\left(10\times k\right)}$

a) k = 2, b) k = 12, c) k = 4

You invest $3500 at an interest rate of 6%pa compounding monthly. How long will it take for your investment to double? Give your answer correct to the nearest month.

months

You are trying to solve the equation..

$3500\cdot\left(1+\frac{6}{\frac{12}{100}}\right)^{x}=7000$

You can use your finance app and solve for n with

n = ? (what you are looking for)

I = 6%

PV = -3500

PMT = 0

FV = 7000

P/Y = 12

C/Y = 12

An investment of $5000 is put in a savings account for 8 years with interest compounding quarterly. At the end the investment is worth $9500. What was the interest rate for the investment? Give your answer to 3sf.

You are trying to solve the equation..

$5000\cdot\left(1+\frac{x}{\frac{4}{100}}\right)^{8\times4}=9500$

You can use your finance app and solve for I with

n = 32

I = ? (what you are looking for)

PV = -5000

PMT = 0

FV = 9500

P/Y = 12

C/Y = 12

You buy are car for $12000. Its value depreciates at 8% a year. What is the value of the car after

a) 1 year

b) 3 years

c) 10 years

Give your answers to 3sf

a) $

b) $

c) $

Use the formula as follows

$12000\cdot\left(1-\frac{8}{100}\right)^{x}$

a) x = 1

b) x = 3

c) x = 10

A new car valued at $25000 depreciates in value at 5% every year. After how many years will the car first be worth less than half of its original value?

years

You are trying to solve the equation...

$25000\cdot\left(1-\frac{5}{100}\right)^{x}=12500$

Enter the function in your GDC

$y=25000\cdot\left(1-\frac{5}{100}\right)^{x}$

Look for the first value of x where the value of the car is less than 12500

You take a loan of $5000 at 3.2%pa compounding monthly, being paid back monthly over a period of 6 years. What are your monthly payments? Give your answer to 2 decimal places. (money)

$ per month

Use your finance app and solve for PMT with

n = 72 (6 x 12 every month for 6 years - this is the number of payments made)

I = 3.2%

PV = 5000

PMT = ? (what you are looking for)

FV = 0 (nothing left when the loan is paid)

P/Y = 12 monthly payments

C/Y = 12 Interest calculated monthly

You take a loan of $8000 at x% pa compounding quarterly, being paid back quarterly over a period of 8 years. Your monthly repayments are $260, what is the interest rate? Give your answer to 2 decimal places.

$ %

Use your finance app and solve for I with

n = 32 (8 x 4 every quarter for 8 years - this is the number of payments made)

I = ? (what you are looking for)

PV = 8000

PMT = -260 (what you are looking for)

FV = 0 (nothing left when the loan is paid)

P/Y = 4 quarterly payments

C/Y = 4 calculated quarterly

...

You are saving for a big trip. You have 3 years to save $10000. A bank offers a savings annuity at 3%pa compounding monthly. How much do you need to put in each month to reach your target? Give your answer to 2 decimal places. (money)

$ per month

Use your finance app and solve for PMT with

n = 36 (3 x 12 every month for 3 years - this is the number of payments made)

I = 3%

PV = 0 (you start with nothing)

PMT = ? (what you are looking for)

FV = 10000 (your target)

P/Y = 12 monthly payments

C/Y = 12 Interest calculated monthly

...

You are given a gift of $20000 to be paid out to you every quarter, with interest compounded monthly over a period of 10 years. The interest rate is 2.5%pa. How much will you receive each quarter? Give your answer to 2 decimal places. (money)

$ per month

Use your finance app and solve for PMT with

n = 40 (10 x 4 every quarter for 10 years - this is the number of payments made)

I = 2.5%

PV = 20000 (your original gift)

PMT = ? (what you are looking for)

FV = 0 (at the end you have received all the money)

P/Y = 4 quarterly payments

C/Y = 12 Interest calculated monthly

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Exam Style Questions - coming soon

The following are exam style questions on this topic that you should try on your own before checking against the video solution.

Question 1

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Question 2

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Question 3

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repeat expandable panels as necessary

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Just for Fun

This session might include an idea for an exploration or a thought provoking question. This section can also be deleted (easily done via the code page) If it has nothing in it it should be deleted

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MY PROGRESS

Self-assessment

How much of 1.4 & 1.7 Compound Interest, Loans and Annuities have you understood?

My notes

IBDP Maths: Applications & Interpretations SL

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1.4 & 1.7 Compound Interest, Loans and Annuities

Compound Interest Slides

Compound Interest Videos

Loans & Annuities Slides

Loans & Annuities Videos

Self Checking Quiz

IBDP Maths: Applications & Interpretations SL

Number and Algebra Home Free Access Weekend! Start here Examination Questions Practice Questions Question Bank Your Graphical Display Calculator Functions Geometry and Trigonometry Statistics and Probability Calculus Pre-IB Preparation Exams & Assessment For Teachers

1.4 & 1.7 Compound Interest, Loans and Annuities

Compound Interest Slides

Compound Interest Videos

Loans & Annuities Slides

Loans & Annuities Videos

Self Checking Quiz

Number and Algebra
Home
Free Access Weekend!
Start here
Examination Questions
Practice Questions
Question Bank
Your Graphical Display Calculator
Functions
Geometry and Trigonometry
Statistics and Probability
Calculus
Pre-IB Preparation
Exams & Assessment
For Teachers