An investor invests £20 000 over three years in a scheme which offers compound interest of 4.5%, compound annually. Which one option gives the amount of money in the scheme after 3 years, rounded to the nearest pound?
A. £22 891
B. £22 700
C. £22 833
D. £22 823
E. £22 800
F. £20 106
G. £22 884
H. £22 929
use 20 000(1.045)^3
To solve this question, we need to calculate the compound interest for the three-year period. The formula for compound interest is given as:
Amount = Principal * (1 + Interest Rate)^Time
In this case, the principal is £20,000, the interest rate is 4.5% (or 0.045 in decimal form), and the time is 3 years. Plugging in these values, we have:
Amount = £20,000 * (1 + 0.045)^3
To calculate this expression, we can follow these steps:
Step 1: Calculate the term inside the parentheses (1 + 0.045)^3
Step 2: Raise the result to the power of 3
Step 3: Multiply the principal (£20,000) by the result from step 2 to get the final amount.
Using a calculator or spreadsheet, we find that (1 + 0.045)^3 is approximately 1.14314 when rounded to five decimal places.
Now, we multiply £20,000 by 1.14314:
£20,000 * 1.14314 = £22,862.80
Rounded to the nearest pound, the amount in the scheme after 3 years is £22,863.
Among the given options, the closest amount to £22,863 is option G: £22,884.
Therefore, the correct answer is G.