Maisie takes out a loan of £840. The loan gathers compound interest at a rate of 4% per month.
How much money will Maisie owe after 2 years?
Give your answer in pounds to the nearest 1p.
Since the interest is compounded monthly and there are 24 months in 2 years, Maisie will have 24 compounding periods.
To start, we need to calculate the monthly interest rate, which is 4%/12 = 0.00333 (rounded to 5 decimal places).
Next, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the amount owed after 2 years
P = the principal amount borrowed (in this case, £840)
r = the monthly interest rate (0.00333)
n = the number of times the interest is compounded per year (12)
t = the time in years (2)
Plugging in the values, we get:
A = 840(1 + 0.00333/12)^(12*2)
A ≈ £965.70
Therefore, Maisie will owe approximately £965.70 after 2 years, to the nearest 1p.
To calculate the amount Maisie will owe after 2 years, we first need to calculate the monthly interest rate. The 4% annual interest rate needs to be divided by 12 to get the monthly interest rate.
Monthly interest rate = 4% / 12 = 0.04 / 12 = 0.00333333 (rounded to 8 decimal places)
Next, we need to calculate the total number of months in 2 years.
Total number of months = 2 years * 12 months/year = 24 months
Now we can use the compound interest formula to calculate the amount owed:
Amount owed = Principal * (1 + interest rate)^number of periods
Amount owed = £840 * (1 + 0.00333333)^24
Calculating this expression, we get:
Amount owed ≈ £840 * (1.00333333)^24 ≈ £898.63
Therefore, Maisie will owe approximately £898.63 after 2 years.