1. Time Value of Money Math
Advanced Level

2. Simple Interest vs. Compound Interest
Interest earned on the principal investment only
Example: You deposit $200 in a 18-month CD and let the money earn interest
Earning interest on the principal and on previous interest earned
Example: you deposit $200 in a money market account that compounds interest quarterly
Principal is the original amount of money invested or saved

3. Simple Interest Equation: Step 1
Prt = I P
Principal r
Interest Rate t
Time Period I
Interest Earned
1,000
.07 5
350.00
$1,000 invested at 7% interest rate for 5 years

4. Simple Interest Equation: Step 2
P+I =FV P
Principal I
Interest Earned FV
Future Value of Investment
$1,000 invested at 7% interest rate for 5 years
1,000
350
$1,350

5. Compound Interest Equations
There are two methods for calculating compound interest
Single deposit investment
Periodic investments
A single sum of money invested once at the beginning of the investment period
Equal amounts of money are invested at regular intervals, such as yearly, monthly, or biweekly

6. Compound Interest Equation – Single Deposit Investment
FV = future value of investment
P = principal or original balance
r = interest rate expressed as a decimal
n = number of times interest is compounded annually
t = number of years
$1,000 invested at 7% interest rate compounded annually for 5 years

7. Compound Interest Equation – Periodic Investments of Equal Amounts
FV = future value of investment
P = periodic deposit amount
r = interest rate expressed as a decimal
n = number of times interest is compounded annually
t = number of years
$1,000 invested every year at 7% annual interest rate for 5 years

8. Comparing Simple versus Compound Interest
Simple Interest = $1,350.00
Compound Interest
for a Single Deposit Investment = $1,402.55
Why are they different?
By reinvesting the interest earned, the interest payment keeps growing as interest is compounded on interest

9. Periodic Investments of Equal Amounts =
Comparing Compound Interest on a Single Deposit versus Periodic Investments
Compound Interest
on a Single Deposit = $1,403.00
Periodic Investments of Equal Amounts =
$5,750.74
To make the most of your money, utilize compound interest and continue to invest!

10. $1,000 invested at 7% for 5 years Amount Investment is Worth
Compound Interest
Number of times interest is compounded has effect on return
Compounding more frequently equals higher returns
$1,000 invested at 7% for 5 years
Compounding Method
Compounded how often?
Amount Investment is Worth
Daily
365
$1,419.02
Monthly 12
$1,417.63
Quarterly 4
$1,414.78
Semi-annually 2
$1,410.60
Annually 1
$1,402.55

11. Let’s Compare: Compound Interest Equation – Single Deposit Investment
$1,000 invested at 7% interest rate compounded annually for 5 years
$1,000 invested at 7% interest rate compounded quarterly for 5 years
Earned $12.23 more because the interest was compounded more frequently

12. Let’s Compare: Compound Interest Equation – Periodic Investments
$1,000 invested every year at 7% annual interest rate for 5 years
$1,000 invested quarterly at 7% annual interest rate for 5 years
Earned $17, more because you contributed to the account quarterly and the interest was compounded more frequently

13. Every variable in the formula impacts the amount of your return
Smart Investing
Every variable in the formula impacts the amount of your return
P = Principal
The larger the principal investment, the greater your return
R = Interest Rate
The higher the interest rate, the greater your return
N = # of Times Interest is Compounded per Year
The more often the interest is compounded, the greater your return.
Rule of Thumb:
The higher the variable, the greater your return
T = Number of Years
The longer you leave your money in the investment, the greater your return

14. Smart Investing OR Which would you choose?
An investment earning compound
interest
An investment earning simple interest OR
Largest return

15. Smart Investing OR Which would you choose?
An investment earning an interest rate of 2%
An investment earning an interest rate of 2.1% OR
Largest return

16. Smart Investing OR Which would you choose?
An investment with an interest rate compounded monthly
An investment with an interest rate compounded yearly OR
Largest return

17. Time Value of Money Math Practice Activities
Choose your practice method
Practice calculating using the step-by-step method
(basic calculator)
Practice calculating by entering all variables into the formula (advanced calculator)

18. Practice calculating using the step-by-step method (basic calculator)
Use with Time Value of Money Math Practice – Basic Calculator Worksheet

19. Time Value of Money Math Practice #1
Camila deposited $ into a savings account one year ago. She has been earning 1.2% in annual simple interest. Complete the following calculations to determine how much Camila’s money is now worth.
Step One: P R T I
600.00
.012 1
7.20
Step Two: P I A
600.00
7.20
607.20

20. Time Value of Money Math Practice #1
How much is Camila’s investment worth after one year?
$607.20

21. Time Value of Money Math Practice #2
Felipe’s grandparents have given him $ to invest while he is in college to begin his retirement fund. He will earn 2.3% interest, compounded annually. What will his investment be worth at the end of four years?
What is the equation?

22. Time Value of Money Math Practice #2
Step One: Divide r n
Step Two: Add 1
.023
.023 1
.023
1.023 1
Step Three: Multiply by exponent
Step Four: Multiply by principal
1.095 4
1.023
1.095
1500

23. Time Value of Money Math Practice #2
What will Felipe’s investment be worth at the end of four years? $

24. Time Value of Money Math Practice #3
Nicole put $ into an account that pays 2% interest and compounds annually. She invests $ every year for five years. What will her investment be worth after five years?
What is the equation?

25. Time Value of Money Math Practice #3
Step One: Divide r
Step Two: Add 1 n
.02 1 1
.02
.02
1.02
Step Three: Multiply by exponent
Step Four: Subtract 1
(1x5)
1.02 1
1.104
1.104
.104
Step Six: Divide by r
Step Five: Multiply by principal n
1.104
2,000
208.16
208.16
.02

26. Time Value of Money Math Practice #3
What will Nicole’s investment be worth at the end of five years?
$10,408.08

27. Time Value of Money Math Practice #4
Robert opens an account at a local bank. The account pays 2.4% interest compounded monthly. He deposits $100 every month for three years. How much is in the account after three years?
What is the equation?

28. Time Value of Money Math Practice #4
Step One: Divide r
Step Two: Add 1 n
.024 12 1
.002
.002
1.002
Step Three: Multiply by exponent
Step Four: Subtract 1
(12x3)
1.002
1.075
1.075 1
.075
Step Six: Divide by r
Step Five: Multiply by principal n
.075
100
7.5
7.5
.002

29. Time Value of Money Math Practice #4
What will Robert’s investment be worth at the end of three years?
$3,750.00

30. Time Value of Money Math Practice #5
When Daisy turned 15, her grandparents put $10,000 into an account that yielded 4% interest, compounded quarterly. When Daisy turns 18, her grandparents will give her the money to use toward her college education. How much will Daisy receive on her 18th birthday?
What is the equation?

31. Time Value of Money Math Practice #5
Step One: Divide r n
Step Two: Add 1
.01
.04 1
.01
1.01 4
Step Three: Multiply by exponent
Step Four: Multiply by principal
1.127
(4x3)
1.01
1.127
10,000
11,270

32. Time Value of Money Math Practice #5
How much will Daisy receive on her 18th birthday?
$11,270

33. Practice calculating by entering all variables into the formula (advanced calculator)
Use with Time Value of Money Math Practice – Advanced Calculator Worksheet
Remember PEMDAS? When entering formulas into an advanced calculator, the order of operations matters. Use parenthesis to group your variables.

34. Time Value of Money Math Practice #1
Camila deposited $ into a savings account one year ago. She has been earning 1.2% in annual simple interest. Complete the following calculations to determine how much Camila’s money is now worth.
Identify the variables
On the calculator, you can save a step. By modifying the formula slightly, you can add the principal while making the interest calculation.
P = 600
r = 1.2% =.012
t = 1
FV = P(1+r)t
Enter the whole formula at once:
600(1+.012)(1)

35. Time Value of Money Math Practice #1
How much is Camila’s investment worth after one year?
$607.20

36. Time Value of Money Math Practice #2
Felipe’s grandparents have given him $ to invest while he is in college to begin his retirement fund. He will earn 2.3% interest, compounded annually. What will his investment be worth at the end of four years?
Identify the variables:
What is the equation?
P = 1500
r = 2.3% =.023
n = 1
t = 4
Enter the whole formula at once:
1500(1+.023/1)^(1x4)

37. Time Value of Money Math Practice #2
What will Felipe’s investment be worth at the end of four years? $

38. Time Value of Money Math Practice #3
Nicole put $ into an account that pays 2% interest and compounds annually. She invests $ every year for five years. What will her investment be worth after five years?
Identify the variables:
What is the equation?
P = 2000
r = 2% =.02
n = 1
t = 5
Enter the whole formula at once:
2000((1+.02/1)^(1x5)-1)/(.02/1)

39. Time Value of Money Math Practice #3
What will Nicole’s investment be worth at the end of five years?
$10,408.08

40. Time Value of Money Math Practice #4
Robert opens an account at a local bank. The account pays 2.4% interest compounded monthly. He deposits $100 every month for three years. How much is in the account after three years?
Identify the variables:
What is the equation?
P = 100
r = 2.4% =.024
n = 12
t = 3
Enter the whole formula at once:
100((1+.024/12)^(12x3)-1)/(.024/12)

41. Time Value of Money Math Practice #4
What will Robert’s investment be worth at the end of three years?
$3,728.90

42. Time Value of Money Math Practice #5
When Daisy turned 15, her grandparents put $10,000 into an account that yielded 4% interest, compounded quarterly. When Daisy turns 18, her grandparents will give her the money to use toward her college education. How much will Daisy receive on her 18th birthday?
Identify the variables:
What is the equation?
P = 10,000
r = 4% =.04
n = 4
t = 3
Enter the whole formula at once:
10000(1+.04/4)^(4x3)

43. Time Value of Money Math Practice #5
How much will Daisy receive on her 18th birthday?
$11,268.25