Can you help with a math question about compound interest?

Asked by JLeslie (65789

) September 25th, 2023

For whatever reason my brain is not functioning on all eight cylinders.

Here is the question: If you have a sum of money, let’s say $100,000, and you have the interest go into a separate account that earns the same interest as the original account, will you have the same amount of total money at the end of five years with two accounts as if you kept all of the money in the original account?

Observing members: 0

Composing members: 0

7 Answers

Identical, within a couple of cents.

Use this calculator

elbanditoroso (33577

)“Great Answer” (2

) Flag as…

Yes, it makes no difference. If p is the principal, i is the interest and t is the time duration, you get (1+i)**n p. If you split p into p=p1 + p2, it works out to the same amount.

LostInParadise (32215

)“Great Answer” (1

) Flag as…

Thanks!

JLeslie (65789

)“Great Answer” (0

) Flag as…

If you want to invest in the Brooklyn Bridge, I can make you a really good deal :-)

elbanditoroso (33577

)“Great Answer” (0

) Flag as…

That formula should have been (1+i)**t p

LostInParadise (32215

)“Great Answer” (0

) Flag as…

Unless your bank unilaterally changes their policy and adds fees or changes rates, as in my experience, they do.

Zaku (30607

)“Great Answer” (1

) Flag as…

In terms of ‘the amount of cash you have’ at the end of the period, most answers are correct: the numbers work out so that the amounts are equal—keeping in mind @Zaku‘s astute observation—but the value of the cash will have been eroded by compounding inflation.

CyanoticWasp (20274

)“Great Answer” (1

) Flag as…