- Higher interest rates indicate that people’s time preference is increasing. That is, that people want money now instead of later because they believe they can earn a greater return on the money and are willing to accept less (discounted at a higher rate). This indicates that the productivity of capital is increasing – the rate of return on the use of that capital is expected to be greater in the future.
- Compounding is the process of extrapolating a future value of a cash flow or series of cash flows at a given interest rate. It determines the future value of those cash flows. Discounting is the opposite, where the present value of future cash flows is determined as of today (or a earlier point in time).
- Simple interest earns a rate of return on an investment at a fixed percentage over time but does not earn interest on the interest. Compound interest allows interest to earn interest by allowing the interest earned to accrue through reinvestment.
- The future value of investment decreases when the interest rate decreases. The present value of an investment increases when the interest rate decreases.
- An ordinary annuity includes cash flows that occur at the end of given time intervals. An annuity due’s cash flows occur at the beginning of the time intervals. An insurance premium paid in advance is an annuity due while a house payment is an ordinary annuity. The timing is significant because of the time value of money. Annuity dues start earning interest earlier (by one period) than ordinary annuities.
- An annuity is a schedule of cash flows that occur at fixed intervals through time until a certain date. A perpetuity is a series of cash flows that continue indefinitely.
- A stock variable has no time dimension. It is simply a number at a particular point in time. A flow variable is a stream of cash flows over time. Examples:
- The amount of cash in your wallet – stock variable
- Monthly social security payments made to senior citizens – flow variable
- The value of your car – stock variable
- The monthly payments on your car – flow variables
- The GNP in the US – stock variable
- Rent on an apartment – flow variable
- Present value decreases when cash flow will occur further in the future. Because you will get the cash flow at a later date than expected (and no interest is accruing), it will be worth less to you when you get it. You have an implicit discount rate and opportunity cost equal to the amount you could have earned on the loan for the additional two months.
- When intra-year compounding occurs, the effective interest rate on an investment is greater than the nominal, or stated interest rate because you will earn interest on your compounded interest. This is also known as the annual percentage rate, or APR. To calculate the effective interest rate, you use the formula (1 + i/m)^mn.
- Capitalization is the process of expressing the stock value of a series of flow values in the future by discounting the cash flows to a present value at a given discount rate. The cash flows are the flow variables and the present value is the stock variable.
- A switch from quarterly to monthly compounding would be in your best interest because it would increase the APR by allowing more interest to be earned on accrued interest.
- NPV is the difference between the present value of the cash inflows and the present value of the cash outflows. In order to determine the present values, you must have a discount rate. The IRR is the discount rate that equates the NPV of cash flows to zero. As such, you don’t need a discount rate because that is what you are trying to calculate. The UAS is a way of expressing a series of uneven cash flows as even cash flows at fixed periods.
- IRR is “internal” because the only information needed to compute it is the magnitude and timing of the cash flows of the loan or asset. No other external information is required.

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