1. ## Interest Comparisons

I have 2 questions which are stumping me.
1)
Which simple interest rate is equal to the annual continuous interest
rate 8% if a certain amount of money is invested for 4 years?
Im having a problem with this one when it comes to the time of money invested. I cannot seem to incorporate this into my solution.

2)Which is rate would be preferred?
Two credit card companies offer 2 different rates for outstanding balance.
1.75% per month.
5.3% quarterly.
By looking at this question I am leaning towards 5.3% quarterly, but I cannot prove it.

Thanks in advance for any help

2. Originally Posted by MatsSundin
I have 2 questions which are stumping me.
1)
Which simple interest rate is equal to the annual continuous interest
rate 8% if a certain amount of money is invested for 4 years?
Im having a problem with this one when it comes to the time of money invested. I cannot seem to incorporate this into my solution.

2)Which is rate would be preferred?
Two credit card companies offer 2 different rates for outstanding balance.
1.75% per month.
5.3% quarterly.
By looking at this question I am leaning towards 5.3% quarterly, but I cannot prove it.

Thanks in advance for any help
Investing your hockey money after retiring, Mats?

1st question: clarify simple interest; no compounding at any time?

2nd question:
1.075^12 = 1.2314....23.14%
1.053^4 = 1.2294.....22.94%
Purty close...both Shylocks

3. Thanks for the response, I figured I would want to make the right decision with my millions, might as well do something right since I couldn't win a cup in Toronto
Anyway, I appreciate your response on the questions. And to clarify I am pretty sure question 1 is implying basic simple interest with a compound each year. A=P(1+rt). I have tried to convert this using Effective rate of interest for compounding interest
Reff=((1+r/n)^n)-1
and Effective rate of interest for continuously compounded interest
Reff=(e^r)-1

neither of these equations incorporate the fact that the investment was for a total of 4 years, telling me this is not the way to go. Any help is appreciated thank you.

4. I think I have figured it out if anyone is interested.
By setting both interest rate formulas equal to each other you can solve for r*

P(1+tr*)=Pe^rt
P's cancel leaving
(1+4r*)=e^(.32) after substitutions
r*=0.0943
r*=9.43%

Thanks for all the help

5. Don't they have an Old Men's Hockey League in Sweden?

OK; cpd continuous after 4 years:
e^(.08 * 4) = 1.3771... a dollar is worth ~1.38

Because of the "4 years" being specified, I'm pretty sure the question
means NO compounding at any time:
the the annual non-cpd rate is simply .3771 / 4 = .094275; ~9.43%

But if we use cpd annually then:
(1 + i)^4 = 1.3771
i = 1.3771^(1/4) - 1 = .08328....; ~8.33%

EDIT: I see you got it...

But you get same results after 1 year cpd continuous:
e^(.08) = 1.08328

So they must mean SIMPLE SIMPLE SIMPLE.... interest.