M2A1 Assignment - Comprehensive Problems

M2A1Textbook Assignment: Comprehensive Problems

From Chapter 3

? Interest and Equivalence

A $5,000 loan was to be repaid with 8% simple annual interest. A total of $5,350 was paid. How long had the loan been outstanding?

? Interest and Equivalence

A company invested $450,000 ten years ago in a new technology that is now worth $1,000,000. What rate of interest did the company earn on a simple interest basis?

? Interest and Equivalence

Suppose that $2,000 is deposited in an account that earns 6% interest. How much is in the account after:

(a) 5 years?

(b) 10 years?

(c) 20 years?

(d) 50 years?

(e) 100 years?

? Interest and Equivalence

The Apex Company sold a water softener to Marty Smith. The price of the unit was $350. Marty asked for a deferred payment plan, and a contract was written. Under the contract the buyer could delay paying for the water softener if he purchased the coarse salt for recharging the softener from Apex. At the end of 2 years, the buyer was to pay for the unit in a lump sum, with interest at a rate of 1.5% per quarter-year. According to the contract, if the customer ceased buying salt from Apex at any time prior to 2 years, the full payment due at the end of 2 years would automatically become due.

Six months later, Marty decided to buy salt elsewhere and stopped buying from Apex, whereupon Apex asked for the full payment that was to have been due 18 months hence. Marty was unhappy about this, so Apex offered as an alternative to accept the $350 with interest at 10% per semi-annual period for the 6 months that Marty had been buying salt from Apex. Which of these alternatives should Marty accept? Explain.

From Chapter 4

? Equivalence for Repeated Cash Flows

For diagrams (a) to (c), compare the unknown values B, C, V, using the minimum number of compound interest factors.

200 200 200 200

0 1 2 3 4

i = 10%

(a) C = value at t = 0

10 10 10 10

0 1 2 3 4 5

i = 10%

(b) V = value at t = 5

100 100 100

0 1 2 3 4 5

i = 10%, n= 5

(c) B = value at t = 0

? Equivalence for Repeated Cash Flows (assume the price of the car does not change over 4 years)

A student is buying a new car. The car’s price is $19,500, the sales tax is 8%, and the title, license, and registration is $650 to be paid in cash. Instead of buying the car now, the student has decided to save money in equal monthly amounts for 48 months and then pay cash. If the student earns 0.75% per month interest on the money she saves, how much money is the monthly savings?

?

? Equivalence for Repeated Cash Flows

Compute E so that the cash flows have a present value of 0.

300 300

200 200 200

100 100

0 1 2 3 4 5 6 7

i = 10%

E E

? Equivalence for Repeated Cash Flows

Helen can earn 3% in her savings account. Her daughter Roberta is 11 years old today. Suppose Helen deposits $4,000 today, and one year from today she deposits another $500. Each year she increases her deposit by $500 until she makes her last deposit on Roberta’s 18th birthday. What is the annual equivalent of her deposits, and how much is on deposit after the 18th birthday?