Question 1189773: A loan of $48,000 is made at 8.75% interest, compounded annually. After how many years will the amount due reach $ 153,000 or more?
Write the smallest possible whole number answer.
Answer by ikleyn(52781)   (Show Source):
You can put this solution on YOUR website! .
A loan of $48,000 is made at 8.75% interest, compounded annually.
After how many years will the amount due reach $ 153,000 or more?
Write the smallest possible whole number answer.
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Use the formula for the annually compounded amount and write this inequality
 >= 153000,
where "t" is the time, in years
Divide both sides by 48000
 >=  = 3.1875.
Take logarithm of both sides
t*log(1.0875) >= log(3.1875) = 0.50345.
Find t
t >=  = 13.82...
Next, you should round this value of t to the closest greatest integer value,
in order for the last compounding was performed.
So, your answer is 14 years.
Solved.
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To see many other similar (and different) solved problems, look into the lesson
- Problems on discretely compound accounts
in this site, and learn the subject from there.
After reading this lesson, you will tackle such problems on your own without asking for help from outside.
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