Simon invested an amount of money in a savings account at 0.5% per annum compound interest.At the end of 3 years, the amount of money in the savings account was £12180.90Work out how much money Simon invested in the savings account.
Question
Simon invested an amount of money in a savings account at 0.5% per annum compound interest.At the end of 3 years, the amount of money in the savings account was £12180.90Work out how much money Simon invested in the savings account.
Solution
To solve this problem, we need to use the formula for compound interest, which is:
A = P(1 + r/n)^(nt)
Where: A = the amount of money accumulated after n years, including interest. P = the principal amount (the initial amount of money) r = annual interest rate (in decimal) n = number of times that interest is compounded per year t = time the money is invested for in years
In this case, we know that A = £12180.90, r = 0.5% or 0.005 (in decimal), n = 1 (since it's compounded annually), and t = 3 years. We need to find P.
So, we can rearrange the formula to solve for P:
P = A / (1 + r/n)^(nt)
Substituting the given values:
P = £12180.90 / (1 + 0.005/1)^(1*3)
P = £12180.90 / (1.005)^3
P = £12180.90 / 1.015075125
P = £12000
So, Simon invested £12000 in the savings account.
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