Final answer:
To find the annual interest rate of the savings account, we use the simple interest formula: I = PRT. Plugging in the values of the principal amount (£13,000), the total interest earned (£6,825), and the time period (15 years), we solve for the interest rate, which is 3.5%, to one decimal place.
Step-by-step explanation:
To calculate the annual interest rate of a savings account that pays simple interest, you can use the formula for simple interest: I = PRT, where I is the interest earned, P is the principal amount (the initial amount of money), R is the interest rate, and T is the time in years.
In this question, the principal amount P is £13,000, the interest earned I is £19,825 - £13,000 = £6,825, and the time T is 15 years.
Now, substitute these values into the simple interest formula and solve for R (the rate):
- I = PRT
- £6,825 = £13,000 * R * 15
- R = £6,825 / (£13,000 * 15)
- R = £6,825 / 195,000
- R = 0.035
The annual interest rate R is 0.035 or 3.5% when expressed as a percentage.
Therefore, the savings account has an annual interest rate of 3.5% to one decimal place.