Question

A sum invested under compound interest doubles itself in 10 years. In how many years will
it become 8 times of the initial amount?
(A)
80 years
(B)
40 years
(C)
30 years
(D) 20 years​

Answer 1

Option (a) 80 years

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Answer 2

Concept Introduction:

Compound interest is computed on the original principle of a deposit or loan, which also takes into account all of the accrued interest from prior periods. The yearly interest rate is raised to the number of compound periods minus one, and the starting principal amount is multiplied by both of these factors.

Given: A sum invested under compound interest doubles itself in $10$ years.

To Find:

We have to find the value of, number of years that will make the amount $8$ times.

Solution:

According to the problem,

$A=P(1+\frac{r}{n})^{nt}$

$2P=P(1+r)^{10}$ ⇒$2=(1+r)^{10}$

Now for P to become $8$ times let the time period be T.

∴ $8P=P(1+r)^{T}$

$2^{3} =(1+r)^{T}$

$[(1+r)^{10}]^{3}=(1+r)^{T} }$

⇒$T=10*3=30$

Final Answer:

The value of number to years for the P to become $8$ times is $30$ years.

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