Are we ever going to use this in real life?

Quantitative Finance Level 1

If your former high school math teacher opens a bank and loans you $1000 at 10% monthly interest (compounded monthly), which of the following is the closest to the amount that you would owe after a year?

Image credit: smbc-comics.com

\$ 2200

\$ 1000 \pi

\$ 1000 e

\$1000

1 solution

Caleb Townsend
Feb 17, 2015

There are $12$ months in a year. At $10\%$ per month, $\$1000 \times 1.1^{12} \approx \$3138$ This is closest to $\boxed{\$1000\pi.}$

It turned out to be a nice coincidence.

Many people chose $\$1000 e$ , presumably because of $P e ^ {rt}$ .

Calvin Lin Staff - 6 years, 3 months ago

This is a bad question. It makes people think there is some correlation between Pi and interest rates. And I agree with the comment above. Most people think of $1000e.

John Kneller - 5 years ago

No. It never said exact. Therefore it could not be $1000e, which is exact.

Zoe Codrington - 2 years, 7 months ago

I took the 10% per a month and converted it to the effective annual rate of (1+(.10/12))^12 = 1.104713067... (10.47%) and multiplied this by the principal of $1,000: $1,000(1.10471) = $1,104.71. Therefore, I chose $1,000 (Yeah, I know that intuitively that does not make sense, but it was the closest answer to $1,105.) What have I done wrong?

Maybe I should have done $1,000 x 1.10471^12 = $3,303.65, but even that is off of $1,000xPi = $3,141.59.

J.J. The Great - 4 years ago

The first line is incorrect. Do you see your mistake?

Note that the statement says: "Paying 10% compound interest month after month is the same as paying 10.5% interest for a year".

Calvin Lin Staff - 4 years ago

What you did wrong was it's 10% a month not 10% a year... So 1+.10 to the 12 no division by 12

Harry Pottash - 2 years, 4 months ago

Are we ever going to use this in real life?

Image credit: smbc-comics.com

1 solution

0 pending reports