1.) Suppose you have $8,900 that you would like to deposit it into a savings acc

Question

1.) Suppose you have $8,900 that you would like to deposit it into a savings account for the next five years. One bank in town offers 4.3% annual interest compounded quarterly, while another offers 4.0% interest compounded continuously. Which bank should you choose, assuming you would like to get the most in interest that you can. 2.) Use the trends and patterns from the notes to derive the formula for effective interest when annual interest rate r is compounded k times per year. Notice we don't know what P is necessarily, and really, it doesn't matter. Can you see why?

Explanation / Answer

1- Principal (P)= $8900

Time (t)=5 years

Rate for bank that compounds quarterly (r) = 4.3%p.a

Amount 1= P((1+r/100)^t) (Let us consider this as amount 1)

Amount 1= P((1+ 4.3/4*100)^20) (Here rate is compounded quarterly, so it is divided by 4 and time in years is multiplied by 4)

Amount 1 = P*(404.3/400)^20 = P*1.01075^20

Rate for bank that compounds continuously (r')=4%

Amount 2= Pe^(rt)

Amount 2= Pe^(20) (Let us consider this as amount 2)

Amount 2= P*2.71828^20

So we, can clearly see that amount 2 is more than amount 1

So we should choose second bank that compounds continuously as it gives better interest.

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