Maximizing Compound Interest: Comparing Weekly and Quarterly Payments

[pbonnie]

Homework Statement

Question is attached.

Homework Equations

sn = [a(1-r^n)]/(1-r)

The Attempt at a Solution

I know the more compounding periods there are, the better. The part that I'm stuck on is what values to put for r and n, since the rate that he is making payments is different from the number of compounding periods. When I use this equation, (using 1 year of payments for example), I'm getting a confusing answer. I used 12 for n, since there are 12 payments being made in 1 year, but I think that's the problem? Since n is supposed to be the number of compounding periods. But then how do I show that there are 12 payments being made?

 

[Mark44]

Homework Statement

Question is attached.

Homework Equations

sn = [a(1-r^n)]/(1-r)

The Attempt at a Solution

I know the more compounding periods there are, the better. The part that I'm stuck on is what values to put for r and n, since the rate that he is making payments is different from the number of compounding periods. When I use this equation, (using 1 year of payments for example), I'm getting a confusing answer. I used 12 for n, since there are 12 payments being made in 1 year, but I think that's the problem? Since n is supposed to be the number of compounding periods. But then how do I show that there are 12 payments being made?

You can't put anything for r, since the interest rate is not given. All you need to do is say whether Harold benefits from the interest calculation being done quarterly vs. being done weekly. To justify your decision, you can ignore the fact that he is putting money in his account monthly, and just compare the two interest schemes: quarterly vs. weekly.

 

[BruceW]

you can work out the change in the equation, due to compounding weekly, while depositing monthly (by carefully thinking about what happens over the course of each month). But as Mark44 says, the question seems to just want a qualitative answer. i.e. a reasonable explanation for why he is better off.

 

[pbonnie]

Oh okay great, thank you both. I was trying to use the equation as a hypothetical situation to show that weekly compounding is better but I guess since it didn't give any other value it's only looking for a word answer.
Thank you :)

 

[Mark44]

Actually, you can do better by showing mathematically that he earns more interest when it's computed weekly vs. quarterly. Just compare the interest earned on $1 for a year with the two methods.