# 3. The Future Value and Present Value of a Single Cash Flow

## d. solve time value of money problems for different frequencies of compounding;

What is the formula to derive the future value of an investment? \(FV_N = PV * (1 + r)^N\) - FV = future value at time N - PV = present value - r = interest rate per period - N = number of years

What is compounding? Compounding is when interest earned is reinvested into the original value so that the next period of interest is applied against a higher value.

What is the formula to derive the present value of some future amount of money? \(PV = \frac{FV_N}{(1 + r)^N}\)

What is a discount rate? The discount rate is just the interest rate used in a present value calculation.

How do you use the BA II Plus Calculator to compute Future/Present Value?
- N = number of periods
- I/Y = Interest rate (10 = 10%, not 0.10)
- PV = Present Value
- FV = Future Value
- To calculate, just enter in the known params, hit `CPT`

and the param you want to compute. E.g. `5 N, 10 I/Y, 100 PV, CPT FV`

= 161.051

What is the future value calculation for rates that compound more than once per year? \(FV = PV \times (1 + \frac{r_s}{m})^(m \times N)\)

What is the future value calculation for an interest rate that is compounded continuously? \(FV = PV \times e^(r_s*N)\) - N is YEARS, not months. So for 18 months, N=1.5

When using the BA II Plus Calculator TVM functions, should the future value (FV) be entered as a positive or a negative? Enter it as a negative, it is seen as a payout.

##### Source:

CFA

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- 115.020.10 Reading 6 - The Time Value of Money to 115.020.10.30 Reading 6 - Time Value of Money - 3. The Value of a Single Cash Flow