**Calculating value of investments**

- Investments change value over a number of years.

- Appreciation is the increase in value of an item. A common example of this is house prices. Each year, the value of a house increases, so we say that its value appreciates. The rate of appreciation is often given as a percentage.

- Depreciation is the decrease in value of an item. A common example of this is car prices. Each year, the value of a car decreases, so we say that its value depreciates. The rate of depreciation is often given as a percentage.

**How to work out appreciation and depreciation**

Compound Appreciation p.a. (a): FV = P (1 + a/100)^{n}

Compound Depreciation p.a. (d): FV = P (1 – d/100)^{n}

**Formula Key:**

FV: Future value

P: Principal

n: number of years

a: appreciation (% increase)

d: depreciation (% decrease

- In order to use these formulae, numbers must be inputted in the correct order.
- The mnemonic BIDMAS is a helpful way of remembering the order of operations (brackets, indices(powers), divide, multiply, add, subtract)

**EXAMPLE**: I have a stocks and shares NISA which increases in value by 20% each year. I originally put in £500, so how much will I have in my account in 5 years’ time?

Compound appreciation:

FV=P (1 + a/100)^{n}

FV= £500 x (1 + 20/100)^{5 }

FV= £500 x (1.2)^{5}

FV= £500 x 2.49 (round to 2 decimal places as currency)

**FV= £1,245**