To determine how much money you would need to put in the bank today to reach your goal of £10,000 in 10 years at a 5% annual compound interest rate, you would use the formula:
FV = PV (1 + r)^n
Where:
FV = future value (the amount you want in the bank in 10 years)
PV = present value (the amount you need to deposit today)
r = interest rate (expressed as a decimal)
n = number of years
Plugging in the known values:
£10,000 = PV (1 + 0.05)^10
To solve for PV, you would divide both sides by (1 + 0.05)^10:
PV = £10,000 / (1 + 0.05)^10
PV ≈ £6,139.
So you would need to deposit £6,139 into the bank today to reach your goal of £10,000 in 10 years at a 5% annual compound interest rate.