1. What’s the FV of an initial $100 after 3 years if i = 10%?1 2 3
10%
100
FV = ?
Finding FVs (moving to the right
on a time line) is called compounding. 6

2. Here’s the setup to find FV:
INPUTS
N I/YR PV PMT FV
OUTPUT
Clearing automatically sets everything to 0, but for safety enter PMT = 0.
2nd, P/Y, 1 ENTER 11

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4. What’s the PV of $100 that will be received in 3 years if i = 10%?
Finding PVs is discounting, and it’s the reverse of compounding. 1 2 3
10%
PV = ?
100 12

5. ( ) Solve FVn = PV(1 + i )n for PV: 1 æ ö PV = $100 ç ÷ è ø 1.10 =3 1 æ ö PV =
$100 ç ÷ è ø
1.10 =
$100 (
0.7513 ) =
$75.13. 13

6. Financial Calculator Solution
N I/YR PV PMT FV
INPUTS
OUTPUT
Either PV or FV must be negative. Here
PV = Put in $75.13 today, take
out $100 after 3 years. 14

7. Calculations using Excel (in edit mode, click on the insert below for Excel)

8. Finding the Time to Double
How many years will it take your $1 investment to equal $2 if the interest rate is 20 percent? … 1 ?
FV = PV(1 + i)n
$2 = $1( )n

9. Financial Calculator
INPUTS
N I/YR PV PMT FV
OUTPUT

10. Calculations using Excel (in edit mode, click on the insert below for Excel)

11. What interest rate would cause $100 to grow to $125.97 in 3 years?1 2 3 i%
The funds grew by 25.97%. Why can’t I just divide by 3 for the yearly rate? Note 25.97% / 3 = %. 26

12. Solution
$100(1 + i )3 = $
INPUTS N
I/YR PV FV
PMT
OUTPUT 26

13. Calculations using Excel (in edit mode, click on the insert below for Excel)

14. What if you were asked for a monthly rate
What if you were asked for a monthly rate? From the prior problem, you know the yearly rate is 8%, can you simply divide 8% by 12 to report a monthly rate of 8%/12 = %? Let’s see…Using the same problem, but asking you to determine in months, we would state “What interest rate would cause $100 to grow to $ in 36 months? Find the monthly rate.” 12 24
36 mo
i%/mo 26

15. Solution
$100(1 + i )36= $
INPUTS N
I/YR PV FV
PMT
OUTPUT 26

16. Calculations using Excel (in edit mode, click on the insert below for Excel)

17. Using the monthly rate, just calculated (0
Using the monthly rate, just calculated (0.6434%), does not equal 8%/12 = %, since dividing assumes that your money does not compound. Almost all accounts compound, so compounding should be used.
A monthly rate, you are given/asked months A quarterly rate, you are given/asked quarters A yearly rate, you are given asked years In the next notes, we will focus on when you can divide a nominal rate (APR) and when you can’t divide, as in an effective annual rate (EAR). 26