Present Value
I want to have $100 in one year. How much do I need to invest now? Interest rate is r per year. I want to have $100 in two years. How much do I need to invest now? ... $100 in three years... ... in T years ... What is the present value of $c to be received in T years, interest rate is r per year?
Present and future values
I will invest $200 at 10% per year one year from now. How much will I have 10 years from now? I want to have $300 15 years from today. How much do I need to invest 2 years from now? Rule: To go forward, multiply, to go back, divide
The same logic
The interest rate is 10% per year I borrow $100 today. How much do I have to repay in 10 years? What about if I borrowed it one year from today? I want to have to pay the bank $100 in 5 years. What amount do I have to borrow today? What amount do I have to borrow one year from now so that I will pay the bank $200 ten years from now
Given $X today: How much will $X be worth in T years if I invest it at r per year? - How much will I have to pay back in T years if I borrow $X today at an interest rate of r per year? What is the future value of $X in T years, given the interest rate? Given $X in T years: How much do I have to save today to have $x in T years if I invest at r per year? How much can I borrow now at r per year so that I have to pay back $X in T years? What is the present value of $X in T years, given the interest rate?
Fun with TVM
The yearly interest rate is 10%. What is the PV of $110 to be received in 1 year? Point: doesn't matter how you do it
The point of it all
The present value of a future cash flow and the future cash flow itself are equivalent What exactly do I mean by equivalent here? My aunt says that when I turn forty, she'll give me $100,000. I want the money now. What do I do? I know I have to buy my girlfriend a $20,000 engagement ring in one year. What do I do?
PV of future CFs
How much that cashflow can be converted to today And so how much that cashflow is worth right now Aunt example How much you need to start with to get an amount in the future Fiancee example And vice versa for future values
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When discounting or finding Future Values, use only effective rates Definition: the effective rate for a period: Tells you how much $1 will become if invested at that rate for 1 such period E.g.: eff