City motors will sell a $15. 000 car for $345 a month for 52 months. what is the interest rate?

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

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

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