Problem Solving

guys please lemme know why in the explanation of this ques in OG, r is taken as 8 to get t.
why they have assumed r = 8, i believe that they've given 2 separate situations, in the first situation r percent interest will double the amount in 70/r years, but in second situation its not the same...
I'm bit confused, please explain..

the main point of the situation is this:

if you invest X dollars at r percent annual interest, compounded annually, your investment will double in 70/r years.

so if the interest rate is 8%, your initial investment will double in 70/8 = 8.75 years.

If Initial investment is given as X dollars. So this means, in 8.75 years, this investment will double to 2X dollars. In the next 8.75 years, the investment will double again to 4X dollars.

Now, the question only requires an approximate value of the investment 18 years from now. You can approximate the investment after 18 years to equal the investment after 2x8.75 = 17.5 years. So 18 years from now is approximately two "doubling periods" at 8% annual interest. Therefore, if the initial investment is for $5000, then after two "doubling periods" , the investment value is a 4 x $5000 = $20,000.

Choose A.

did I clear your doubt?

-BM-

yes, thanks a lot for a nice explanation.
I was confused with rate r, but when i read ur explanation, i got it..
thanks again..