Question

Question #1 (25 Points):

A company is planning to make equal quarterly deposits into a bank account. They want their account to have 2 million dollars after 5 years from now because they want to buy a certain machine. Note that the first quarterly deposit is made today and the last deposit is made at the end of year 5.

A) If the bank’s interest rate is 15% per year compounded monthly, how much should the company deposit each quarter? (12.5 points)

B) If the bank’s interest rate is still 15% per year but compounded continuously, how much should the company deposit each quarter? (12.5 points)

Answer 1

t = 5*4 = 20 quarters

There are total 21 deposits (now + 20 more)

a.

i = 15%/12 = 1.25% per month

Effective interest rate per quarter = (1+0.0125)^3 - 1

= (1.0125)^3 - 1

= 0.037970703

Quarterly deposit = 2000000*(A/F,3.7970703%,21)

= 2000000* 0.037970703/((1 + 0.037970703)^21-1)

= 2000000* 0.037970703/((1.037970703)^21-1)

= 2000000*0.031983611

= 63967.22

b.

i = 15%/4 = 3.75% per quarter

Effective interest rate per quarter = e^0.0375 - 1

= 0.038211997

Quarterly deposit = 2000000*(A/F,3.8211997%,21)

= 2000000* 0.038211997/((1 + 0.038211997)^21-1)

= 2000000* 0.038211997/((1.038211997)^21-1)

= 2000000*0.031899293

= 63798.59