Exploring Present Value

4. The April 1972 issue of Consumer Reports suggested that a homebuyer purchase a washing machine, dishwasher, and clothes dryer from a department store that charged $675 plus 15% interest each year for two years rather than having the builder install them. The builder in this example could get the appliances for $450, but he would add this amount on to the mortgage. If the mortgage matured in 27 years (the national average in 1972) and if the mortgage rate of interest was 7.75%, the appliances would cost a total of $1075. The total cost of the appliances purchased at the department store on a two-year contract would be $785. Explain why the advice of Consumer Reports is bad advice in this case.

5. Suppose you want to retire in 45 years with $1,000,000 and the interest rate is 5%. Use the present value calulator at:
http://www.moneychimp.com/calculator/present_value_calculator.htm
to determine how much money you would need right now in order to achieve this goal. Then use this calculator to see how much you would need right now if the interest rate is 9% (which is about the historical return on funds invested in a diversified portfolio of stocks.)

6. The interest rate formula that computes the future value of present sums given the interest rate is: Future Value = Present Value*(1 + Interest Rate)(Number of years) or F=P(1+r)n Given any three of the four values, we can compute the missing one (though computing the number of years can be pretty challenging). Use this formula in the problems below.
5. Suppose that the interest rate is now 3%.
a) If you have $1000 now, how much will it be worth in one year if invested at this interest rate? $
b) If you have $1000 now, how much will it be worth in TWO years if invested at this interest rate? $
c) Use this formula to find what amount of money now would grow into $1545 one year from now at 3% interest. $
d) If you are promised $1545 one year from now, what is the value of that promise today, that is, what amount of money right now has the same value if the interest rate is 3%? $
6. Suppose that your rich uncle gives you an interest-free loan of $10,000 for one year. Your rich aunt gives you a gift of $1000 now. Your grandfather promises you $1200, but you will not get it for two years. Which is the most valuable? We cannot tell until we compute the present value of each. Let us do the computations assuming that the interest rate is 10%.
e) What is the present value of your grandfather's gift? $
f) What is the value of your uncle's gift? $
I will do the easy one. The present value of your aunt's gift is $1000.
g) The gift that is most valuable is that from your ?? uncle aunt grandfather and the least valuable is that from your ?? uncle aunt grandfather .
But what if the interest rate is only 5% Will the ranking still be the same? Let's find out. I will do the easy one: your aunt's gift still has a present value of $1000.
h) Your grandfather's gift is now worth: $
i) Your uncles gift is now worth: $
j) The gift that is now most valuable is that from your ?? uncle aunt grandfather and the least valuable is that from your ?? uncle aunt grandfather .

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