one bank pays 5.5% annual interest, while a second bank pays 4.5% annual interest.determine how much longer it will take to accumulate at least $50,000 in the second bank account if you deposit $1000 initially and $1000 at the end of each year.

Question

one bank pays 5.5% annual interest, while a second bank pays 4.5%  annual interest.determine how much longer it will take to accumulate at least $50,000 in the second bank account if you deposit $1000 initially and $1000 at the end of each year.

phi · Answer

You could use $$ FV= pymt\cdot \frac{(1+i)^n-1}{i} $$ From http://en.wikipedia.org/wiki/Time_value_of_money#Future_value_of_an_annuity Here, Future Value is 50,000 payment is 1000 i is the interest rate as a decimal (e.g. 0.055 for 5.5% and 0.045 for 4.5%) you must solve for n the number of years you can use logarithms to find n

nastech · Answer

thanks a lot

phi · Answer

thank me after you get the answer

nastech · Answer

thanks I got the answer to be 26.78yrs

phi · Answer

That looks good for 4.5%  but the question is
determine how much longer ...
so you have to do the same for 5.5% and subtract the two times

nastech · Answer

oh okay, I'm doing that now, thanks for correcting me

nastech · Answer

eureka!!!! I got the final answer to be 2.09yrs

phi · Answer

yes, that is what I got.

nastech · Answer

Thanks a lot and may God bless you