Question

if your investment becomes 3 times the original amount in 8 times . in how many years it will be 6 times ?​

Answer 1

The time after which investment becomes 6 times the original amount is 13 years  .

Step-by-step explanation:

The investment becomes 3 times the original amount in 8 times .

Let The initial investment = p

The final investment =A = 3 p

Time period = t = 8 years

Let The rate = r

According to question

Final investment = initial investment × $(1+rate)^{time}$

i.e  A = p  × $(1+r)^{t}$

Or, 3 p = p × $(1+r)^{8}$

∴  $(1+r)^{8}$  = 3                     .................1

Again

Let The investment becomes 6 times the original amount in T years .

So, Final investment = initial investment × $(1+rate)^{time}$

i.e  A = p  × $(1+r)^{t}$

Or, 6 p = p × $(1+r)^{T}$

∴  $(1+r)^{T}$  = 6                     .................2

Or, eq 2 can be written as

putting power $\dfrac{1}{T}$   both side

Or, 1 + r = $(6)^{\dfrac{1}{T}}$

So, from eq 1

$6^{(\dfrac{1}{T})^{8}}$  = 3

i.e  $6^{\dfrac{8}{T}}$ = 3

Taking Log both side

Log $6^{\dfrac{8}{T}}$  = Log 3

Or, $\dfrac{8}{T}$  ×  0.77 = 0.47

Or, $\dfrac{8}{T}$  = $\dfrac{0.47}{0.77}$

Or, $\dfrac{8}{T}$  = 0.6

∴  T = $\dfrac{8}{0.6}$

i,e  T = 13.33  years

So, The time after which investment becomes 6 times the original amount = T = 13 years

Hence, The time after which investment becomes 6 times the original amount is 13 years  . Answer