Question

Please read the questions carefully. Please draw the cash flow diagrams and explain the steps that you are going to approach to solve the problems then solve the problem. Show the details in solving the problems. Please write legible hand writing, otherwise there is a deduction from your grade 10 points Missing Cash Flow Diagram is deductible points equal to 10% of the total points for each question. Question - 1 A series of equal semiannual cash flows starts with the first cash flow occurring on January 1, 1991 and ends with the last cash flow occurring on January 1, 2008. Each cash flow is equal to S128,000. The nominal interest rate is 12% and compounding is semiannual. What single amount on July 1,2001, is equivalent to this cash flow system? Question 2) • The purchase of the car that Joe dreams about can be accomplished by making payments of $300 a January 1, 2001. The financing company charges 6% nominal interest rate compounded monthly. Joe wants to be able purchase the car for cash on January 1,1995, just after he graduates from college. Joe has a job and started making depositing of $275 each month into an account that pays9% compounded monthly beginning with the first deposit on February 1,1990. The last deposit is to be made on January 1,1995. Will Joe have saved up enough money to purchase the car? If not, how much should Joe be saving each month if all other conditions remain the same? Q3) Joe Show off bought a Mercedes when he came to Tech as an engineering student (so that his feet would not get cold on the way to those early morning classes). The Mercedes was purchased by making a loan that was to be paid off in 20 equal, quarterly payments. The interest rate on the loan was 12% per year with quarterly compounding. After four years, at the time that Joe made his 16th payment, he got married (too many dates!) and sold the Mercedes to his buddy Sam Pledge. Sam made arrangements with Joe's bank to refinance the loan and to pay Joe's unpaid balance by making 16 equal quarterly payments at the same interest rate that Joe was paying. After 3 k years, at the time that Sam made his 13th payment, Sam flunked out too many dates!) and sold the car to Nancy. Nancy paid the bank $2,000 cash (she had a good summer job!) to pay the loan balance. What was the amount of Joe's loan to purchase the Mercedes when it was new?

Answer 1

1). Cash flow diagram:

$128,000 $128,000 $128,000 $128,000 $128,000 $128,000 $128,000 IIIIIII t=0 t= 1 t -2 t=32 t = 33 t = 34 t = 35

Number of payments made from 1 Jan 1991 to 1 Jan 2008 = 35

Interest rate = 12%/2 = 6%

Amount deposited = 128,000

Amount accumulated on 1 Jan 2008: PMT = 128,000; N = 35; rate = 6%; Type = 1 (as it is annuity due), solve for FV.

Value = 15,119,470.93

For a single amount deposited on 1 Jul 2001 to be equal to this value on 1 Jan 2008, we have:

FV = 15,119,470.93; N = 14; rate = 6%; Type = 1, solve for PV.

Amount to be deposited on 1 Jul 2001 is 6,687,356.57