Having hard time with this.... Help?????

Question

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

Answer 1

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