Question

1. You are about to deposit $569 into one of the following savings accounts to be left on deposit for 25 years. Each bank offers an account with a different interest rate and compounding period. Assuming you want to maximize your wealth, how much money would be in the bank account that offers the best effective rate of return after 25 years?

Bank A: 9.5 percent rate compounded semi-annually

Bank B: 9.4 percent rate compounded monthly

Bank C: 9.3 percent rate compounded daily

Bank D: 9.2 percent rate compounded continuously

Answer 1

Ans- calculation of effective interest rates:-

Formula E= (1+I/n)ⁿ - 1

Bank A - 9.5% compounding semi annually

E =[ (1+0.095/2)² -1]× 100 = 9.726%

Bank B -9.4% compounding montly

E= [(1+0.094/12)¹² - 1] × 100. = 9.816%

Bank C - 9.3% compounding daily

E= [(1+0.093/365)³⁶⁵ -1]× 100 = 9.745%

Bank D = 9.2% compounding continuously

Formula for this E = e^{​​​​​​i}​​​​​ - 1

= e^{​​​​​​0.092} - 1

= 0.09636 . = 9.636%

Calculation of amount in bank after 25 years on the basis of best effective rate of return:

The best effective rate of return is 9.816 i.e, montly compounding i.e, BANK B-

Amount in bank account after 25 years in bank B:-

Amount = P(1+E)ⁿ

   = 569(1+0.09816)²⁵    = $5912.25

The money would be in the bank account that offers the best effective rate of return i.e, bank B after 25 years is 5912.25