Math Is Fun Forum

Easy.

remember the formula for compound interest??The formula is A=P(1+r/100)^t where A is total amount ,p is principal amount,r is rate of interest and t is time.So for this question A for the first month will be A=k(1+0.5/100)^1 = k(100.5/100) = k(1.005).

Similarly for second month it will be A= k(1+0.5/100)^2 = k(1.005)^2 and so on.

If u notice we get a geometric progression if we keep on adding.Therefore at the end of nth month money in bank =

(1.005k +1.005^2k + 1.005^3k +......+1.005^nk) = k(1.005 + 1.005^2 + 1.005^3......+1.005^n)

Now for the no of months when the account has 100k will be when the sum of terms inside the bracket above is 100.So applying sum of GP formula we get :

1.005(1.005^n-1)/1.005-1 = 1.005(1.005^n-1)/0.005 = 201(1.005^n -1 ) = 201 * 1.005^n -201

Now this value should be equal to 100.So

201*1.005^n -201 = 100
1.005^n = 301/201

1.005^n = 1.4975

From here u will get N to be approximately 80 months.SO thats the anwer