Final answer:
Matt deposited £2500 which earns compound interest quarterly at a rate of 0.58%. Using the compound interest formula, the amounts at the end of each quarter are calculated and the final balance after 12 months would be £2558.53.
Step-by-step explanation:
Matt deposited £2500 in a Standard account that earns compound interest at a rate of 0.58% every 3 months. To calculate compound interest, the formula used is A = P(1 + r/n)nt, 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), n is the number of times that interest is compounded per year, and t is the time the money is invested for in years.
Using this formula, the calculations for each 3-month period would be as follows:
- First 3 months: A = £2500(1 + (0.0058/4))1 = £2514.50
- Second 3 months: A = £2514.50(1 + (0.0058/4))1 = £2529.08
- Third 3 months: A = £2529.08(1 + (0.0058/4))1 = £2543.76
- Fourth 3 months: A = £2543.76(1 + (0.0058/4))1 = £2558.53
The interest earned in the third 3 months is £2543.76 - £2529.08 = £14.68, and the interest in the fourth 3 months is £2558.53 - £2543.76 = £14.77. Therefore, the final value after 12 months is £2558.53.