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?