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?

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

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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.

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.

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