Answer: Step 1: Understand the problem
Daniel takes out a loan of £830, and the loan gathers compound interest at a rate of 3% per month. We need to find out how much money Daniel will owe after 2 years.
Step 2: Convert the monthly interest rate to a decimal
The monthly interest rate is 3% = 0.03. We'll use this decimal value in our calculations.
Step 3: Calculate the number of months
Since we're interested in finding the amount owed after 2 years, we need to convert the time period to months. There are 12 months in a year, so:
2 years × 12 months/year = 24 months
Step 4: Calculate the future value of the loan
We can use the formula for compound interest:
A = P(1 + r)^n
Where: A = future value of the loan P = principal amount (initial loan) = £830 r = monthly interest rate = 0.03 n = number of months = 24
A = 830(1 + 0.03)^24
Step 5: Calculate the result
Using a calculator or software, we get:
A ≈ 1241.41
So, after 2 years, Daniel will owe approximately £1241.41.
Step-by-step explanation:
