Question
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?
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?
Answers
GPT 3.5
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.
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.