Find out how long it takes a $3400 investment earn $300 interest

Question

Find out how long it takes a $3400 investment to earn $300 interest if it is invested at 8% compounded semi annually. Round to the nearest 10th of a year. A=P(1+r/n)^nt

Answer 1

The investment will be worth 3700 when it has earned 300 in interest.

8% compounded is semiannually is equivalent to 4% every 6 months

So 3700 = 3400 x 1.04^2t

3700/3400 = 1.04^2t

37/34 = 1.04^2t. Now take the log of both sides

log(37/34) =log 1.04^2t

log(37/34) = 2t log1.04

t= Log(37/34)/2log1.04

t= 1.0779 = 1.1rounded to nearest 10th

Answer 2

300 = 3400(1 + 0.08/2)^2t

300/3400 = (1.04)^2t

log(3/34) = 2tlog(1.04)

t = log(3/34)/2log(1.04)

t = 15.4 years