Mathematical finance

ebayissues

Hi all


could someone help me with this.


An investor has two options. She can invest her money in a deposit account with bank A and earn interest which is continuously compounded at a nominal rate of 6%. Alternatively she can invest her money with bank B that offers semi-annual compounding at a nominal rate of 6%. Although the effective rate of interest is higher on the second option the investor is indifferent between the two accounts because the nominal rates are equal.

bah1011

Not quite sure what you are asking for but,

continuously componded €1 at %6 would be 1.0618 after a year. APR of 6.18%. Formula is e^.06

semi annual would be 1.0609 or APR 6.09%.
Formula (1+.06/2)^2

TiGeR KiNgS

bah1011 wrote: »

Not quite sure what you are asking for but,

continuously componded €1 at %6 would be 1.0618 after a year. APR of 6.18%. Formula is e^.06

semi annual would be 1.0609 or APR 6.09%.
Formula (1+.06/2)^2

This is correct.

The more times the principal amount is compounded in a time period the return diminishes but still increases as demonstrated above.

whysomoody

To conclude, she should obviously invest in Bank A as they real return is higher.

ebayissues

bah1011 wrote: »

Not quite sure what you are asking for but,

continuously componded €1 at %6 would be 1.0618 after a year. APR of 6.18%. Formula is e^.06

semi annual would be 1.0609 or APR 6.09%.
Formula (1+.06/2)^2

I would i be able to solve this as i'm preparing for my exams.

can you please expalian continously compounded as to how you got those figures.

thanks you very much for your replies and patience

bah1011

e is exponential http://en.wikipedia.org/wiki/Exponential_function

.06 is the interest rate. If you had €100 euro it would be 100e^.06

^ is to be power of..

whysomoody

easiest way to explain it is this.

Imagine you start with 10,000, and the interest is 15%

when you get the interest it is now worth 11500. if you were to get 15% on that it would obviously be higher again etc.

With continuous compounding you are effectively being credited with the interest you earn immediately and the next period you earn the interest on the principal and added interest so the effective rate is higher.

i.e. you could get 15% at the end of the year = 11500 or you could get 7.5% for 6 months worth 10750 and another 7.5% at the end worth 11,556.25.

The difference is 56.25 which is the 7.5% earned on the interest.

ebayissues

bah1011 wrote: »

e is exponential http://en.wikipedia.org/wiki/Exponential_function

.06 is the interest rate. If you had €100 euro it would be 100e^.06

^ is to be power of..

Thank you very much.

its much appreciated.