Answer: B. 16.72 years
Step-by-step explanation:
If interest is compounded bi-monthly, the formula to calculate the accumulated amount (A) is given by:-
, where P = principal , r= rate of interest, x= time period(years).
[1 year =12 months, total periods in 12 months if period per month is 2 = 2 x 12 =24]
Given: P= 1000, A= 2000, r= 4.15% = 0.0415
Substitute all values in formula , we get
![1000\times (1+\dfrac{0.0415}{24})^{24x}=2000\\\\\Rightarrow\ (1.00172916667)^{24x}=2\\\\\text{Taking log on both sides, we get}\\\\\Rightarrow \ln(1.00172916667)^{24x}=\ln2\\\\\Rightarrow 24x\ln(1.00172916667)=\ln2\\\\\Rightarrow\ x=\dfrac{\ln 2}{24\ln(1.00172916667)}\approx16.72\ years](https://tex.z-dn.net/?f=1000%5Ctimes%20%281%2B%5Cdfrac%7B0.0415%7D%7B24%7D%29%5E%7B24x%7D%3D2000%5C%5C%5C%5C%5CRightarrow%5C%20%281.00172916667%29%5E%7B24x%7D%3D2%5C%5C%5C%5C%5Ctext%7BTaking%20log%20on%20both%20sides%2C%20we%20get%7D%5C%5C%5C%5C%5CRightarrow%20%5Cln%281.00172916667%29%5E%7B24x%7D%3D%5Cln2%5C%5C%5C%5C%5CRightarrow%2024x%5Cln%281.00172916667%29%3D%5Cln2%5C%5C%5C%5C%5CRightarrow%5C%20x%3D%5Cdfrac%7B%5Cln%202%7D%7B24%5Cln%281.00172916667%29%7D%5Capprox16.72%5C%20years)
Hence, option B. is correct.