Folder:
115 CFA
File:
115.020.10.30 Reading 6 - Time Value of Money - 3. The Value of a Single Cash Flow

# 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.

• CFA