I have just tried to put together a formula for savings which is attached below.
I have it for such a question
I put in a lump sum amount of £3,500 into a new account. I also will be paying £900 of my wage per month into this account for 5 years. The gross interest rate will be 5%. How much will I end up with after this time?
where the answer is
γ = £3,500
α = 0.05
t = 5
β = £900
F = (( £3,500 )(exp^(0.05x5))) + (( £900 )(( exp^(0.05x5)) - 1)/( exp^(0.05/12)) -1 ))
F = (3500 x (1.284)) + ((900 x (((1.284) – 1)/((1.004)-1))
F = 4494.089 + (900 x (68.024))
F = 4494.089 + 61221.767
F = £65,715.86
Therefore I will have saved £65,715.86.
Firstly is this formula correct? Because I have noticed in this calculator SAVINGS CALCULATOR ... I am getting a different figure. I have noticed that this Halifax calculator is missing the final months interest. So the question is, is my formula right? and if so can someone help me in re-arranging this formula, to solve for t and to solve for β as it is giving me a headache.