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:
![\[ A = P \left(1 + (r)/(n)\right)^(nt) \]](https://img.qammunity.org/2021/formulas/mathematics/high-school/afqdilx2t2c5taxlzn1q6eltry86vq5iqk.png)
Where:
-
is the future value of the investment,
-
is the principal amount (initial investment),
-
is the annual interest rate (as a decimal),
-
is the number of times interest is compounded per year,
-
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:
![\[ A = 2000 \left(1 + (0.02)/(1)\right)^(1 * 3) \]](https://img.qammunity.org/2021/formulas/mathematics/high-school/gv8ogs278mgh6emddidf0t05l639mlcq3a.png)
Calculate the expression:
![\[ A = 2000 * (1.02)^3 \]](https://img.qammunity.org/2021/formulas/mathematics/high-school/8p20m6fq8zyd57jo2p1pfxkjoxtvmptsyw.png)
![\[ A = 2000 * 1.061208 \]](https://img.qammunity.org/2021/formulas/mathematics/high-school/pat0ve0lm854rcd6xf0f2ib2hzs443f1lf.png)
A = £2122.416
£2122.42
So, the investment would be worth approximately £2122.42 after 3 years with a 2% annual interest rate compounded annually.