Compounding

[wiishesssss]

You have two investment options for your $18,000 wedding gift. The first bank offers 8% compounded semiannually (2x a year) and the 2nd bank offers 7.5% compounded monthly (12x a year).

part 1) If you left the money in the account for 1 year ..which bank would be the better investment?

part 2) how many years would it take for the 1st bank to become the better investment?



thank you for anyone who can help me out

so far i got:

part 1)

B = P (1 + r/n) ^ (nt)

B = 18,000 (1 + .08/2) ^ (2 x 1) = 19468.8

and

B = P(1+ r/n) ^ (n x t)
B = 18,000 ( 1 + .075/12) ^ (12 x 1) = 19397.39


so i got that Bank 1 (8% ; compounded semiannually) would be the better investment if you left the money in the account for 1 year

 

[Denis]

Correct.

Part 2 doesn't make much sense as a question:
1st bank is already the better investment !

And it will remain the better of the 2, since effective annual rate is higher:
(1 + .08/2)^2 = ~1.0816 : 8.16%
(1 + .075/12)^12 = ~1.0776 : 7.76%

 

[wiishesssss]

I completely agree ...
but according to part b i'm looking for a year ... any ideas?

 

[Denis]

I completely agree ...
but according to part b i'm looking for a year ... any ideas?

Well then, answer is 1st year :idea: