Dennis invested £1000 for four years into a savings account. He received 5% per annum compound interest. Calculate the total interest he earned over the four years.
Answer (2)
Apply the compound interest formula: A = P ( 1 + r ) t .
Calculate the amount after 4 years: A = 1000 ( 1 + 0.05 ) 4 = 1215.50625 .
Subtract the principal from the final amount to find the interest: I n t eres t = A − P = 1215.50625 − 1000 = 215.50625 .
Round the interest to two decimal places: £215.51 .
Explanation
Problem Analysis Let's analyze the problem. Dennis invested £1000 in a savings account with a 5% annual compound interest rate for 4 years. We need to calculate the total interest he earned over these four years.
Compound Interest Formula We will use the compound interest formula to find the amount after 4 years: A = P ( 1 + r ) t , where:
A is the amount after t years
P is the principal amount (£1000)
r is the annual interest rate (5% or 0.05)
t is the number of years (4)
Calculating the Amount After 4 Years Substitute the given values into the formula: A = 1000 ( 1 + 0.05 ) 4 A = 1000 ( 1.05 ) 4 A = 1000 × 1.21550625 $A = 1215.50625
Calculating the Total Interest Now, calculate the total interest earned by subtracting the principal amount from the amount after 4 years: Interest = A − P Interest = 1215.50625 − 1000 Interest = $215.50625
Final Result Rounding the interest to two decimal places, we get £215.51.
Examples
Understanding compound interest is crucial in personal finance. For example, when planning for retirement, knowing how your investments grow over time with compound interest helps you estimate your future savings. Similarly, when taking a loan, understanding compound interest allows you to calculate the total repayment amount, including the principal and accumulated interest. This knowledge empowers you to make informed financial decisions, whether it's choosing the right investment strategy or managing debt effectively.
Dennis earned a total interest of £215.51 from his £1000 investment over four years at a 5% annual compound interest rate. This was calculated using the compound interest formula. The final amount after four years is £1215.51, and the interest earned is the total amount minus the initial investment.
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