City Motors will sell a $15,000 car for $345 a month for 52

months. What is the interest rate? 9.10 percent 8.38 percent 9.28 percent 8.67 percent 8.53 percent

Answer: 8.38%

$15000 is the PV of the annuity $345 for 52 months discounted at

the required rate.

Hence,

15000 = 345*((1+r)^52-1))/((r*(1+r)^52))

43.47826

The value of r (monthly interest) can be found out be trial and

error, so that the value of the RHS of the above equation is

43.47826

if r is taken as 1%

=(1.01^52-1)/(0.1*1.1^52) | 40.394194 |

=(1.01^52-1)/(0.1*1.1^52) | 40.394194 | ||

if r is taken as 0.6% | |||

=(1.006^52-1)/(0.006*1.006^52) | 44.555958 | ||

if r is taken as 0.7% | |||

=(1.007^52-1)/(0.007*1.007^52) | 43.461009 | ||

exact rate will be 0.6 + 0.1(44.555958-43.47826)/(44.555958-43.461009) = |
0.69842449 | ||

8.38109391 |