### 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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