Question

£2000 is invested with an interest rate of 2% per year. How much is the investment worth after 3 years

Answer 1

£2122.42

Explanation:

To find the answer, use the compound interest formula:

A = P ( 1 + (r/n) ) ^ (n*t)

A = 2,000 ( 1 + (0.02/1) ) ^ (1*3)

A = 2,000 ( 1 + 0.02 ) ^ 3

A = 2,000 ( 1.02 ) ^ 3

A = 2,000 ( 1.061208 )

A = about 2122.2 pounds

Okay THIS is right. I'm so sorry.

Answer 2

The investment would be worth approximately £2122.42 after 3 years with a 2% annual interest rate compounded annually.

How did we get the value?

To calculate the future value of an investment with compound interest, you can use the formula:

`\[ A = P \left(1 + (r)/(n)\right)^(nt) \]`

Where:

-
`\( A \)` is the future value of the investment,

-
`\( P \)` is the principal amount (initial investment),

-
`\( r \)` is the annual interest rate (as a decimal),

-
`\( n \)` is the number of times interest is compounded per year,

-
`\( t \)` is the number of years.

In this case:

- P = £2000,

- r = 0.02 (2% expressed as a decimal),

- n (compounding frequency) is not specified, so let's assume it's compounded annually n = 1,

- t = 3 years.

Substitute these values into the formula:

`\[ A = 2000 \left(1 + (0.02)/(1)\right)^(1 * 3) \]`

Calculate the expression:

`\[ A = 2000 * (1.02)^3 \]`

`\[ A = 2000 * 1.061208 \]`

A = £2122.416

`\[ A \approx` £2122.42

So, the investment would be worth approximately £2122.42 after 3 years with a 2% annual interest rate compounded annually.