SOLUTION: Sydney buys a new car for $22,000 and finances the car for 5 years at 3% interest compounded yearly. She estimates that the value of the car will decrease by 14% each year. If Sy

Algebra ->  Customizable Word Problem Solvers  -> Finance -> SOLUTION: Sydney buys a new car for $22,000 and finances the car for 5 years at 3% interest compounded yearly. She estimates that the value of the car will decrease by 14% each year. If Sy      Log On

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Question 1139659: Sydney buys a new car for $22,000 and finances the car for 5 years at 3% interest
compounded yearly. She estimates that the value of the car will decrease by 14% each
year. If Sydney is able to sell the car on the day of her last car payment for the value she
estimated, how much money will she have spent over the 5 years?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Use compound interest formula with
yearly compounding:
+A+=+A%5B0%5D%2A%28+1+%2B+r+%29%5Et+
+A+=+22000%2A%28+1+%2B+.03+%29%5E5+
+A++=+22000%2A1.03%5E5+
+A+=+22000%2A1.159274+
+A+=+25504.03+
The interest plus principal over 5 years is:
$25,504.03
--------------------
The depreciated value of the car after 5 yrs:
+A+=+A%5B0%5D%2A%28+1+-+.14+%29%5E5+
+A+=+22000%2A.86%5E5+
+A+=+22000%2A.47043+
+A+=+10349.39+
$10,349.39
----------------------
Over the 5 years, she has spent:
+25504.03+-+10349.39+=+15154.64+
$15,154.64