Question

You have $100,000 to invest into a bank.  Bank A offers 17% compounded monthly. Bank B offers 16.5% compounded quarterly.  How much more money will you have in Bank A after two years?

Answer 1

Case I: When $100,000 is invested in Bank A

interest rate = 17%

Compounded Monthly

Monthly interest rate = 17%/12 = 1.416667%

In 2 years no. of monthly periods = n = 2*12 = 24

Future value of C = 100000 in 2 years will be

FV = C*(1+r)ⁿ = 100000*(1+1.416667%)²⁴ = 140159.962419529

Case II: When $100,000 is invested in Bank B

interest rate = 16.5%

Compounded Quarterly

Quarter interest rate = r = 16.5%/4 = 4.125%

In 2 years no. of monthly periods = n = 2*4 = 8

Future value of C = 100000 in 2 years will be

FV = C*(1+r)ⁿ = 100000*(1+4.125%)⁸ = 138178.385917622

Difference between the money in Bank A and that in Bank B = 140159.962419529 - 138178.385917622 = 1981.576502

We will have $1981.58 more in Bank A than Bank B

Answer -> 1981.58 (Rounded to 2 decimals)