Brain Teasers
Of Great Interest
The Bank of Tasmania was offering a special deal for new customers. "Open a new account and deposit $1 with us for 1 year and we will give you 100% interest." was the offer.
Now Jimbo, being quick to spot a deal popped in to see the manager and enquired, "Can I have my interest added quarterly?"
"Why not?" said the manager.
"What about monthly?" suggested Jimbo.
"OK", said the manager.
"How about daily...hourly...by the minute....?"
"OK...OK...OK, whatever", said the manager.
Jimbo was quite pleased with this deal.
What is the maximum amount (rounded to the nearest cent) that Jimbo could find in his account at the end of the year?
Now Jimbo, being quick to spot a deal popped in to see the manager and enquired, "Can I have my interest added quarterly?"
"Why not?" said the manager.
"What about monthly?" suggested Jimbo.
"OK", said the manager.
"How about daily...hourly...by the minute....?"
"OK...OK...OK, whatever", said the manager.
Jimbo was quite pleased with this deal.
What is the maximum amount (rounded to the nearest cent) that Jimbo could find in his account at the end of the year?
Answer
Compound Interest = P(1+r)^nP=1 ($1). Since rate = 100% , r = 1.
For n periods per annum, rate is therefore r = 1/n
The limit as n approaches infinity of (1 + 1/n)^n = e (exponential growth constant) = 2.71828..
Jimbo would have at the most $2.72 to the nearest cent.
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Comments
I was amused to see that I rated it very fun and very easy -- exactly the opposite of what had been there before. That's my math background, I guess. I like math. Thanks for the puzzle.
Too bad you couldn't plop more loot into the account....
Nice teaser.
Silly me, didn't slow down enough to see that the answer was just going to be e and punched (1 + 1/527040)^527040 into my calculator.
Silly me, didn't slow down enough to see that the answer was just going to be e and punched (1 + 1/527040)^527040 into my calculator.
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