What's the interest rate if the principal is $6000, the balance is $43,257.41 and the time is 20 years and compound quarterly?

The interest rate is 10% compounded quarterly. You use this common TVM formula to find the rate:

FV=PV[1 + R]^N

43,257.41=6,000[1+R/4]^(20*4) you would use logs to find the interest rate.

R=2.50% per quarter x 4 =10% comp. quarterly.

43,257.41=6,000[1+R/4]^(20*4) divide both sides by 6000.

7.2095683=[1 + r]^80 take the log of both sides.

Log(1+r)=10^0.010723865

1+r=1.025

r=1.025 - 1

r=.025 x 100

r=2.50%