A saver puts 1000 rupees in an account that pays 100% interest a year…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A saver puts rupees in an account that pays interest a year. If the interest is added times a year, in equal parts, the amount after one year is rupees. A bank clerk asks what happens if the interest is added more and more often. Find the amount when the interest is added times a year, to two decimal places. Then find the limit of the amount as grows without bound, to two decimal places.
Need a reminder? The key ideaShow
. If and , then . Remove by a common denominator or by a conjugate.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Given. Amount rupees.
Plan. Put , then use the limit that defines .
Step 1. For . , so the amount is rupees.
Step 2. The limit. , so the amount tends to rupees.
Check. More frequent interest helps, but only a little: from rupees for yearly interest to at most rupees, however often it is added.
Answer: rupees with additions, and at most rupees.
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