7000=4000(1+x/12)^156

Question

Please Help do not understand how to solve

Answer 1

7000=4000(1+x/12)¹⁵⁶ looks like a compound interest equation, 156 being the number of months in 13 years. x looks like the annual percentage interest rate and interest is compounded monthly.

(1+x/12)¹⁵⁶=7000/4000=7/4=1.75 (growth rate).

156log(1+x/12)=log(1.75) (logs to any base).

log(1+x/12)=log(1.75)/156=0.001558 approx. (using logs arbitrarily to base 10).

1+x/12=10^0.001558=1.0036 approx., so so x/12=0.0036, x=0.043=4.3%.

We could have used natural logs but the result would have been the same.