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Financial Economics - Compounding and Present Value

1. Compounding: Suppose someone invested 2 dollars on January 1, 1776 at 3.3 percent interest compounded yearly.
a) How much interest would the investment be worth on January 1, 2001 (225 years later)?
b) Suppose the interest rate were 6.6 percent instead of 3.3 percent. What would the investment be worth?
c) Suppose the interest rate was 6.6 percent in even years and 3.3 percent in odd years. How much would the investment be worth?

2. Present value: Suppose you are considering two job offers from investment banks. Their offers are different in that:
a) investment bank 1 promises to pay you 60,000 dollars per year and a signing bonus.
b) investment bank 2 promises to pay you 65,000 dollars per year but no signing bonus.
What is the minimum signing bonus you would ask of investment bank I to accept their offer? In calculating it, assume that:
- All dollar amounts above are certain and are adjusted for inflation.
- The real rate of interest is 3 percent.
- You plan to work for either bank for exactly 5 years before going to business school.
- You get the signing bonus today and you get your annual salary at the end of each year.

Solution Preview

1. PV = 2 and interest rate = 3.3%
a) Number of years = 225
Compute FV = PV * (1+r)^n= 2 * (1+3.3%)^225 = $2975.79

b) When r = 6.6%, we compute
FV = PV * (1+r)^n= 2 * (1+6.6%)^225 = $ 3,518,852.40

c) We could combine the interest of two adjacent years
For every two years, the interest is ...

Solution Summary

In just under 230 words, this solution demonstrates how to solve for compound and present value. All calculations are shown and this is done in a step-wise manner.