The MBA Math Monday series helps prospective MBA students to self assess their proficiency with the quantitative building blocks of the MBA first year curriculum.
As described in the first and second MBA Math Monday finance exercises, quantitative finance builds incrementally. Those exercises deal with converting a single amount of money at one point in time into a different single amount at a different time. This exercise deals with converting multiple cash flows into a single cash flow. With this step, and the issues that it raises about rates and timeframes, finance supports the efforts of business people everywhere to capture the current value of future financial prospects as well as the efforts of individual and institutional investors to make current investments that will generate future cash flows.
Constant annuities, which are a set of equal periodic payments, are incredibly common, especially in the credit markets. If you’ve ever taken out a loan to buy a car or house or finance your education with student loans, you’ve sold an annuity. You get money upfront and the lender receives a stream of constant payments from you. The inability of the world’s largest financial institutions to correctly value subprime mortgage annuities was the trigger to the ongoing financial meltdown.
What is the present value of an annuity in which $300 is paid each year for 4 years, assuming a discount rate of 8% and the first payment is received one year from now?
Solution (with audio commentary): click here