Future values and continuous compounding Here are two useful rules of thumb. The “Rule of 72” says that with discrete compounding the time it takes for an investment to double in value is roughly 72/interest rate (in percent). The “Rule of 69” says that with continuous compounding the time that it takes to double is exactly 69.3/interest rate (in percent).
If the annually compounded interest rate is 12%, use the Rule of 72 to calculate roughly how long it takes before your money doubles. Now work it out exactly.
Can you prove the Rule of 69?
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Annuities Use Excel to construct your own set of annuity tables showing the annuity factor for a selection of interest rates and years.
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Declining perpetuities and annuities You own an oil pipeline that will generate a $2 million cash return over the coming year. The pipeline's operating costs are negligible, and it is expected to last for a very long time. Unfortunately, the volume of oil shipped is declining, and cash flows are expected to decline by 4% per year. The discount rate is 10%.
What is the PV of the pipeline's cash flows if its cash flows are assumed to last forever?
What is the PV of the cash flows if the pipeline is scrapped after 20 years?
