$$\DeclareMathOperator{cosec}{cosec}$$

# Number and Algebra

## Furthermore

Official Guidance, clarification and syllabus links:

Examination questions may require the use of technology, including built-in financial packages.

The concept of simple interest may be used as an introduction to compound interest.

Calculate the real value of an investment with an interest rate and an inflation rate.

In examinations, questions that ask students to derive the formula will not be set.

Compound interest can be calculated yearly, half-yearly, quarterly or monthly.

Link to: exponential models/functions in topic 2.

Formula Booklet:
 Compound interest $$FV = PV \times \left( 1 + \frac{r}{100k} \right) ^{kn},$$ $$FV$$ is the future value, $$PV$$ is the present value, n is the number of years, $$k$$ is the number of compounding periods per year, $$r$$% is the nominal annual rate of interest

Compound interest is a fundamental concept in finance where the interest accrued on an amount of money is added to the original principal, forming a new base on which subsequent interest is calculated. This process allows interest to be earned on previously accumulated interest, leading to the amount growing exponentially over time.

The key formula for compound interest is:

$$FV = PV \times \left( 1 + \frac{r}{100k} \right) ^{kn} \\ \text{where:} \\ FV \text{ is the future value of the investment/loan, including interest} \\ PV \text{ is the principal investment amount (the initial deposit or loan amount)} \\ r \text{ is the annual interest rate (r=6 means six percent)} \\ n \text{ is the number of years} \\ k \text{ is the number of times the interest is compounded per year.}$$

For example, let's consider a principal amount (PV) of £1000, with an annual interest rate (r) of 5%, compounded quarterly (k=4) for 1 year (n=1). Using the compound interest formula, the future value (FV) would be calculated as follows:

$$FV = £1000 \times \left( 1 + \frac{5}{400} \right) ^{4} \\ FV = £1000 \times (1.0125)^4 \\ FV \approx £1050.95$$

So, the investment would grow to approximately £1050.95 after one year with quarterly compounding.

If you use the TI-Nspire graphic display calculator here are instructions for using the Finance Solver.

This video on Compound Interest and Depreciation is from Revision Village and is aimed at students taking the IB Maths Standard level course

This video on Finance Solver is from Revision Village and is aimed at students taking the IB Maths Standard level course.

Show the Futurama clip called 4.3 billion dollars and get students to check the maths. Yes it is true!!!

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