Find how long it takes a $1600 investment to earn $200 interest if it is invested a 6% interest compounded quarterly $200 interest will be earn in approximately years ????? (round to the nearest tenth) A=P ( 1+ R/N) nt

A = P(1 + r/n)

^{nt}We want A = P + $200. We know n=4 (quarterly compounding), r = 0.06 (6% as a decimal). Find t.

1600+200 = 1600(1 + (0.06/4))

^{4t}1800 = 1600(1.015)

^{4t}1.125 = (1.015)

^{4t}[Divided both sides by 1600]To get the t out of the exponent, take the log of both sides. You can use any base log. I'll use the natural log (ln):

ln(1.125) = ln(1.015

^{4t})ln(1.125) = 4t*ln(1.015) [ln(a

^{b}) = b*ln(a)]ln(1.125)/4ln(1.015) = t [Use your calculator to find the logs]

**1.977 = t ≈ 2 years**