a) 7 years

b) 8 years

c) 9 years

d) 10 years

correct answer is: c) 9 years

**Explanation**

*We can do this math using 2 methods –*

i) **Using log formula:**

Let,

Principal = ‘p’

Rate = 8 % p.a.

Time = ‘n’

According to the question,

Amount = ‘2p’

We know,

Amount = p\left[1+\left(\frac{r}{100}\right)\right]^n

\rightarrow2p=p\left[1+\left(\frac{8}{100}\right)\right]^n

\rightarrow\frac{2p}{p}=\left(\frac{100+8}{100}\right)^n _{[interchange & L.C.M]}

\rightarrow2=\left(\frac{108}{100}\right)^n

\rightarrow2=\left(1.08\right)^n

Now, find the ‘n’ value we use **log formula**.

So,

log\ 2 = log\ (1.08) ^{n}

\rightarrow log\ 2 = n\ log\ (1.08)

\rightarrow 0.301 =\ n\times\ 0.0334 _{[put the log value]}

\rightarrow\ n=\frac{0.301}{0.0334}

\rightarrow\ n=9.01

\therefore Time almost 9 years.

ii) **Another method is ‘The rule of 72’ formula:***The ‘ Rule of 72‘ helps to know how long it will take to double any money from an investment. It’s an easy formula based on a set yearly return rate.*

The formula for the Rule of 72 is:

\frac{72}{compound\ interest\ rate}

Here, C.I. Rate = 8 % p.a.

\therefore Years need =\frac{72}{8} or 9 years.**Ans:** A sum of money will double in 9 years at 8% compound interest per annum.

**Another way to ask this same question is:****1. Calculate the time required for a sum of money to double at an 8% compound interest rate per annum.****2. How long will it take for an investment to double at a compound interest rate of 8% per annum?****3. Determine the number of years needed for a principal amount to double with an 8% compound interest rate per annum.****4. Find out in how many years a sum of money will double with an 8% annual compound interest rate.****5. If the compound interest rate is 8% per annum, what is the time taken for a sum of money to double?**