### GIGAMIND

# 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