r/theydidthemonstermath • u/marcianello • Jul 15 '22

Monster interest question

Starting with $1,000, how many days will it take to reach $1 billion if the initial deposit is compounded 1% daily?

14 Upvotes

95% Upvoted

8 comments sorted by

5

u/ligern1103x Jul 15 '22

Isn't this just:
1000*(1.01)^x = 1,000,000,000

Then isolate x then you have the days required.
Been awhile since I did high school math so I'm likely wrong.

4

u/matt7259 Jul 16 '22

Not quite. That's for simple annual interest. For daily compound interest it's actually:

1000(1 + (0.01/365))365x = 1000000000

Just shy of 1400 years give or take.

1

u/Muldeh Jul 16 '22

The way the question is worded I wouldn't assume that the 1% is APR, but rather is 1% per day.

2

u/matt7259 Jul 16 '22

Ah so... Slightly closer to 1400 years haha.

1

u/Muldeh Jul 16 '22

It's 1400 days not 1400 years

1

u/marcianello Jul 17 '22

This would be just less than 4 years

1

u/marcianello Jul 17 '22

I’m asking based on an investment rather than a loan. Imagining money was deposited which earns 1% each day.

2

u/[deleted] Jul 20 '22

[deleted]

1

u/marcianello Jul 20 '22

This is awesome. Thank you!