Question

Problem 1: You save $5,000 dollars in year 1. $5,150 dollars in year 2. If the amounts increase 3% a year through year 20, how much money will you have at the end of year 20 at 10% interest?

Problem 2: A smart engineer wants to save now and play later. She wants to retire in 20 years with $1.5 million dollars of play money. At 10% per year interest, to reach the $1.5 million goal, starting 1 year from now, she must invest how much money annually?

Problem 3: You receive a gift of $25,000 dollars and have come up with three options on how to spend the money. 1) Buy a new car even though you do not need it. 2) Invest the money in a company stock option that has an expected value increase at 20% a year. However, this option is fairly risky. 3) You can put the money a saving account at 6% year. If you decide to buy the new car, what is the opportunity cost with the choice? If you invest the money in the stock, what is the opportunity cost? What is an opportunity cost?

Problem 4: You have been invited to go Oktoberfest. You buy a passport for $100 dollars and it is valid for 10 years. The next day, the trip gets cancelled. Is your passport a suck cost or an opportunity cost? What is a suck cost?

Problem 5: A new engineer graduate plans to buy a business for $100,000 dollars at 10% interest per year. The loan payment each year to pay off the loan in 7 years is what amount?
  

Answer 1

Problem 1:

Money I will have at the ned of 20 years = $351,528

Working:

Formula for future value of a growing annuity is given below.
P=5,000 r=10% or 0.1 g= 3% or 0.03 n = 20 Future value = 5,000 x ((1+0.10)^20 - (1+0.03)^20)/(0.10-0.03) = 5,000 x (6.7275 - 1.8061)/(0.07) =5,000 x (4.9214/0.07) =5,000 x 70.3056 = 351528
Problem2: Amount to be saved each year for acheiving a final saving of $1.5 million after twenty years = $26,189 Formula for annuity required to get a desired future value is P= FV (r) / ((1+r)^n - 1) Where P = annual savings FV = Future value r = Rate of interest n= number of years For our probem P= 1,500,000(0.10)/ ((1+0.10)^20-1)    = 150,000 / (6.7275 - 1)    = 150,000 / 5.7275    = 26,189

Problem 3:

Opportunity cost is the best alternative which is lost by taking up a course of action.

If decision to buy a car is taken, opportunity cost is the next best alternative, that is to invest in stock market which gives a return of 20%..

If decision to invest in stock market is taken, opportunity cost is the next best alternative, that is to put the money in a saving account which gives 6% per annum.

Problem 4:

Suck cost is the cost which is necessary to be incurred, and which does not have a bearing on decisions to be taken.

The cost of the passport of $100 is a suck cost, as this cost will not be material for any decision taken in future. And this cost is necessary cost for any future travel.