UPSC CDS 2 2021 Math Paper

Let the sum be P and interest rate be r% per annum.
Time, n=5yr
(Compounded annually)
A=2P As we know the formula,
A‌‌=P(1+‌

r

100

)n
⇒2P‌‌=P(1+‌

r

100

)5
⇒2‌‌=(1+‌

r

100

)5
⇒21∕5‌‌=1+‌

r

100

... (i)
‌ Now, Sum ‌=P
A=4P
‌ Time ‌=n‌ years ‌
‌ Again using, ‌A=P(1+‌

r

100

)n
⇒4P=P(1+‌

r

100

)n
⇒4=(21∕5)n‌ [From Eq. (i)] ‌
⇒22=2n∕5
On comparing the powers with same base, we get
2=‌

n

5

⇒n=10
Hence, the sum will become four times in 10yr.