Question

How long should $1,000 be invested compounded

bimonthly to produce a final balance of $2,000 at
4.15%?
A. 16.70 years
B. 16.72 years
C. 16.76 years
D. 16.73 years

Answer 1

Answer: B. 16.72 years

Explanation:

If interest is compounded bi-monthly, the formula to calculate the accumulated amount (A) is given by:-

`A=P(1+(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* (1+(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=(\ln 2)/(24\ln(1.00172916667))\approx16.72\ years`

Hence, option B. is correct.