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Sachi buys a couch and a love seat for $4800. She pays $500 and finances the rest at $156.54 per month for 3 years. What annual interest rate, compounded monthly, is Sachi being charged? Round your answer to two decimal places.

Julius  Jun 16, 2017
edited by Julius  Jun 16, 2017
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 #1
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Sachi buys a couch and a love seat for $4800. She pays $500 and finances the rest at $156.54 per month for 3 years. What annual interest rate, compounded monthly, is Sachi being charged? Round your answer to two decimal places.

 

$4,800 - $500 = $4,300 Amount Financed.

PMT=PV. R.{[1 + R]^N/ [1 + R]^N - 1}

$156.54 =$4,300.R{[1 + R]^36 / [1 + R]^36 - 1}

P.S. There is no DIRECT or algebraic way of solving for interest rate. However, iteration and interpolation are used to get closer and closer to the actual rate. After doing that half a dozen times, I got: 1.5416667 per month or: 1.5416667 x 12 =18.5% compounded monthly.

Guest Jun 16, 2017
 #2
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+1

If you hve tables Julius you may be able to use them backwards to find the approximate interest rate.

Melody  Jun 16, 2017
 #3
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+1

@Melody I have this calculator that calculates the interest for me, but I'm not good at plugging in. http://www.zenwealth.com/businessfinanceonline/TVM/TVMCalculator.html

Julius  Jun 16, 2017
 #4
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May I ask, what type of calculator do you have? It should have these keys:

N     I%YR     PV     PMT       FV

 

Make sure N is in MONTHS for this problem. Enter 36 under N.

Enter $4,300 under PV

Enter zero(0) under FV

Enter $156.54 under PMT. You may have to make it negative or -$156.54.

Solve for I%YR. It should give you the interest rate per month. Just multiply by 12 to give you annual interest rate compounded monthly. Depending on the calculator, it may give you annual interest rate.

Just try it and see if you get the same rate that I got above. Good luck.

Guest Jun 16, 2017
 #5
avatar+206 
+1

@Guest 

I'm not sure if you're the same human who keeps helping me, but you have helped me sooo much! Thank you :)

Julius  Jun 17, 2017
 #6
avatar+90134 
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Julius, I tried using your calculator and it refused to work out the nominal (or any other) interest rate.

Maybe you'd do better with a different calculator. :/

Melody  Jun 17, 2017
 #7
avatar+90134 
+1

Hi again Julius,

I just tried a different calculator and it would not do it either.

 

You may have to leave out the Payment and then  'guess' the interest rate, you guess will get closer and closer until it is within the desired 2 decimal places.

 

I shall try it with your calculator....

 

PV = 4800-500 = 4300

Periods = 36

monthly

FV=0

 

The PMT that you want is $156.64  but you cannot put that in.

You have to try different rates (these are nominal annual rates) until you find the one that will give you a PMT of $156.64.

 

nominal annual rate tested % PMT (payment found)  
10 138.75 Too little
15 149.06 Too little
18 155.46 Too little
19 157.62 Too big
18.5 156.54 Too little
18.55 156.64 exact
     

 

 

So to two decimal places the nominal rate is 18.55%  and that is using your calculator :)

Melody  Jun 17, 2017
 #8
avatar+206 
0

Thank you for all your help, it didn't work because you have to make the present value negative. :P I got the same value as you when I did that. 

Julius  Jun 18, 2017

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