Cynthia invests some money in a bank which pays 5% compound interest per year.
She wants it to be worth over £8000 at the end of the 3 years. what is the smallest amount, to the nearest pound, she can invest?
First, we need to use the compound interest formula to calculate the future value of the investment:
FV = PV x (1 + r)^t
Where:
FV = Future Value (which is £8000)
PV = Present Value (the amount Cynthia needs to invest)
r = Annual interest rate (5% or 0.05)
t = Number of years (3)
Plugging in the values, we get:
8000 = PV x (1 + 0.05)^3
8000 = PV x (1.157625)
Now, divide both sides by 1.157625 to solve for PV:
PV = 8000 / 1.157625
PV ≈ £6912.62
Therefore, Cynthia needs to invest at least £6912.62 to have over £8000 at the end of 3 years. The smallest amount she can invest is £6913.