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Trish invests $5,000 in her IRA in a bond trust that pays 9%....

Trish invests $5,000 in her IRA in a bond trust that pays 9% interest compounded quarterly. Sean invests $5,000 in his IRA  in a certificate of deposit that pays 8.9% compound continuously. who has more money after 20 years, Trish or Sean? After 20 years Trish will have ?  After 20years, Sean will have? Who will have more money after 20years? Trish or Sean?
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2 Answers

compounded investment
A = a(1+r/n)nt
 
A: a return
a: invested money
r: annual interest
n: compounding frequency per year
t: number of year
 
when n →∞, then 
 
A = a*exp(rt)
 
 (1) Sean
Quarterly compounded (9% annual interest): A = 5000*(1+0.09/4)4*20
                                                                     = 29,651
(2) Trish
continuously compounded (8.9% annual interest): A= 5000*exp(0.089*20)
                                                                           = 29,649
 
Practically, they will have the same money in 20 yrs. 

Comments

It always answer comes slightly different when used base ten vs, base e.

Comment

5000 ( 1+ 0.09/4) 20(4) = 29650,73  Trish
 
 5000 ( 1 + 0.089)20  = 27, 571 2.34   Sean
 
        Might have been the opposite, because Trish has higher interest rate and compound quarterly.