Question

How long should $1,000 be invested compounded

Answer 1

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:-

$A=P(1+\dfrac{r}{24})^{24x}$ , 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

$1000\times (1+\dfrac{0.0415}{24})^{24x}=2000\\\\\Rightarrow\ (1.00172916667)^{24x}=2\\\\\text{Taking log on both sides, we get}\\\\\Rightarrow \ln(1.00172916667)^{24x}=\ln2\\\\\Rightarrow 24x\ln(1.00172916667)=\ln2\\\\\Rightarrow\ x=\dfrac{\ln 2}{24\ln(1.00172916667)}\approx16.72\ years$

Hence, option B. is correct.