Henry Devine bought a new dishwasher for $320. He paid $20 down and made 10 monthly payments of $34. What actual yearly interest rate did He

320-20=300 that is how much he borrowed.

34*10=340 that is how much he paid back (the principal) in 9 months.  He paid $40 interest in 3/4 of a year

If it is simple interest then

I=Prt

40=340*r*(3/4)

40=340*0.75*r

r=40/(340*0.75)

$${\frac{{\mathtt{40}}}{\left({\mathtt{340}}{\mathtt{\,\times\,}}{\mathtt{0.75}}\right)}} = {\frac{{\mathtt{8}}}{{\mathtt{51}}}} = {\mathtt{0.156\: \!862\: \!745\: \!098\: \!039\: \!2}}$$        

That is about 15.7%  per annum