Andrew invests £4500 in a savings account for 2 years. The account pays compound interest at a rate of 3.4% per year. Calculate how much Andrew has in this savings account at the e... Andrew invests £4500 in a savings account for 2 years. The account pays compound interest at a rate of 3.4% per year. Calculate how much Andrew has in this savings account at the end of the 2 years. Read more

Steps to Solve

1. Identify the Compound Interest Formula

The formula for compound interest is given by:

$$ A = P (1 + r)^t $$

where:

• ( A ) is the amount of money accumulated after n years, including interest.
• ( P ) is the principal amount (the initial amount of money).
• ( r ) is the annual interest rate (decimal).
• ( t ) is the time the money is invested for in years.

2. Substitute the values into the formula

Given:

• Initial investment ( P = £4500 )
• Interest rate ( r = 3.4% = 0.034 ) (convert percentage to decimal)
• Time ( t = 2 ) years

Substituting these values into the formula:

$$ A = 4500 (1 + 0.034)^2 $$

3. Calculate the value inside the parentheses

First, calculate ( 1 + 0.034 ):

$$ 1 + 0.034 = 1.034 $$

4. Raise the sum to the power of 2

Next, we calculate ( (1.034)^2 ):

$$ (1.034)^2 = 1.068856 $$

5. Final Calculation

Now, multiply by the principal amount ( P ):

$$ A = 4500 \times 1.068856 $$

Calculate this product:

$$ A \approx 4810.852 $$

So, rounding to two decimal places, we have:

$$ A \approx 4810.85 $$