interest rate. PLEASE help.?

Question

what interest rate is required in order that your money will trible in the next 20 years with semi annual compounding?

could someone please help me with this. thanks.

Answer 1

If the rate is r%, the annual increase is x (1+ r/100). So you need to find r, such that (1+r/100)^20 = 3. In other words the 20th root of 3.

If interest is paid twice a year, then you do the same, except that you need the 40th root of 3 every 6 months. The question then arises as to whether the annual rate is based on twice the 6-monthly rate, or (1+r/100)^2. There isn't a big difference, but you can guarantee that banks will always quote the larger figure!

Answer 2

= (1 + [0.055691911303382/2])^(20 * 2)
= (1 + 0.027845955651691)^40
= 3

Answer: 5.5691911303382% per annum compounded semi-annually for 20 years.

Answer 3

let
a = initial amount
r = rate
n = 20yrs
you need to solve
3a = a(1+r)^(2n)
3 = (1+r)^40
so
r = 3^(1/40) - 1 = 0.0278 = 2.78% compounded semi-annually

note: 3^(1/40) means the 40th root of 3

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