Question

12. Problem 5.36 Click here to read the eBook: Future Values Click here to read the eBook: Present Values Click here to read the eBook: Semiannual and Other Compounding Periods NONANNUAL COMPOUNDING a. You plan to make five deposits of $1,000 each, one every 6 months, with the first payment being made in 6 months. You will then make no more deposits. If the bank pays 8% nominal interest, compounded semiannually, how much will be in your account after 3 years? Round your answer to the nearest cent. b. One year from today you must make a payment of $10,000. To prepare for this payment, you plan to make two equal quarterly deposits (at the end of Quarters 1 and 2) in a bank that pays 8% nominal interest compounded quarterly. How large must each of the two payments be? Round your answer to the nearest cent. $

Answer 1

A)

Since there are 5 deposits are being made every 6 months of $1000 0 0 3 Year 1.5 1000 0.5 1000 2 1000 2.5 1000 Cash flow 1000 Bank pays 8% nominal Interest rate compounded semiannually effective annual Interest rate= (1+0.08/2)^2-1 0.0816 = 8.16% Value at the end of year 3= 1000*(1.0816)^2.5 +1000*(1.0816)^2 +1000*(1.0816)^1.5 +1000*(1.0816)^1 +1000*(1.0816)^0.5 5632.98

B)

The payment to be made after 1 year is = $10,000 Nominal rate of interest= 8% compounded quarterly Hence rate of Interest per quarter = 2% The payment has to be made in two equal instalments Let's divide this 1 year period into 4 quarter period and let's assume X is the quarterly payment. Q1 = X Q2=X Now, Q1 X is being invested for 3 periods (quarter), Q2 is being invested for 2 periods X*(1+0.02)^3 + x*(1+0.02)^2 = 10,000 Solving this equation for the value of X We get X = 4758.26