2. A QUICK DOUBLE CHECK
Calculator set to 4 decimal places
Calculator set to END (2nd PMT/BGN key)
Calculator is set to 1 payment/yr (P/Y)
3. A quick review: a single deposit
FV = PV (1 + i)n
What your money will grow to be
PV = FV [1/(1 + i)n ]
What your future money is worth today
Inflation adjusted interest rate:
(1+i)/(1+r) -1
Substituting i* for i when controlling for inflation
4. What will John’s $100,000 grow to be in
15 years if he leaves it in an account
earning an 8% rate of return.
PV = -100,000
I/Y = 8
N = 15
CPT FV = 317,216.91
5. Annuities: multiple payments
Definition -- a series of equal dollar
payments coming at the end of a certain
time period for a specified number of time
periods (n).
Examples – mortgages, life insurance
benefits, lottery payments, retirement
payments.
6. Compound Annuities
Definition -- depositing an equal sum of
money at the end of each time period for a
certain number of periods and allowing the
money to grow
Example – having $50 taken out of each
paycheck and put in a Christmas account
earning 9% Annual Percentage Rate.
7. Future Value of an Annuity
(FVA) Equation
This equation is used to determine the
future value of a stream of deposits/
payments (PMT) invested at a specific
interest rate (i), for a specific number of
periods (n)
For example: the value of your 401(k)
contributions.
8. SOLVING FOR FUTURE VALUE
OF AN ANNUITY (MULTIPLE)
The future value is the unknown
CPT FV
9. Calculating the Future Value
(FVA) of an Annuity:
Assuming a $2000 annual contribution
with a 9% rate of return, how much will
an IRA be worth in 30 years?
FVA = PMT {[(1.09)30 – 1]/.09}
FVA = $2000 {[13.27 - 1]/.09}
FVA = $2000 {[12.27]/.09}
FVA = $2000{136.33}
FVA = $272,610
11. Solving for Future value:
Each month, Anna N. deposits her
paycheck ($5,000) in an account offering a
monthly interest rate of 6%. How much
will Anna have in her account at the end of
1 year?
13. Practice Problems
If Jenny deposits $1,200 each year into a
savings account earning an Annual Rate
of return of 2% for 15 years, how much will
she have at the end of the 15 years?
How much will she have if she deposits
$1,200 each month? How much will she
have if she earns interest monthly?
15. Extreme Caution!
Make double sure your time frames are
consistent……..
Ifthe payment is a monthly payment; then the
compounding rate of return has to be a
monthly rate of return.
Example: A 15% ANNUAL rate of return is
equal to a monthly rate of return of 1.25%
15/12 = 1.25
17. Present value (moves backward) &
Future value (moves forward)
In real life: Winning
the lottery (present
value) or saving for
retirement (future
value)
18. Present Value of an Annuity
(PVA) Equation
This equation is used to determine the
present value of a future stream of
payments, such as your pension fund or
insurance benefits.
19. SOLVING FOR PRESENT VALUE
OF AN ANNUITY (MULTIPLE)
The Present Value is the unknown
CPT PV
20. Present Value of an Annuity: An
example: Alimony
What is the present value of 25 annual
payments of $50,000 offered to a soon-to-be
ex-wife, assuming a 5% annual discount rate?
(PVA is the only unknown)
PVA = PMT {[1 – (1/(1.05)25)]/.05}
PVA = $50,000 {[1 – (1/3.38)]/.05}
PVA = $50,000 {[1 – (.295)]/.05}
PVA = $50,000 {[.705]/.05}
PVA = $50,000 {14.10}
PVA = $704,697 lump sum if she takes the
pay off today!
22. Future Value Annuity of that
divorce settlement
25 annual payments of $50,000 invested
@ 5% results in
$2,386,354.94
A difference of:
$1,681,354.94
23. Amortized Loans
Definition -- loans that are repaid in equal
periodic installments
With an amortized loan the interest payment
declines as your outstanding principal declines;
therefore, with each payment you will be paying
an increasing amount towards the principal of
the loan.
Examples -- car loans or home mortgages
24. Solving for the PMT
No more hypothetical “what ifs”
You can really use this stuff!
26. Buying a Car With 4 Easy Annual
Installments
What are the annual payments to repay $6,000 at
15% APR interest? (the payment is the unknown)
PVA = PMT{[1 – (1/(1.15)4)]/.15}
$6,000 = PMT {[1 – (.572)]/.15}
$6,000 = PMT {[.4282/.15]}
$6,000 = PMT{2.854}
$6,000/2.854 = PMT
$2,102.31 = Annual PMT
28. Buying the same car with monthly
payments
PVA = PMT{[1 – (1/(1.0125)48)]/.0125}
$6,000 = PMT {[1 – (.55087)]/.0125}
$6,000 = PMT {[.44913/.0125]}
$6,000 = PMT{35.93}
$6,000/{35.93} = PMT
$166.99 = monthly PMT
http://www.bankrate.com
29. Extreme Caution!
Make double sure your time frames are
consistent……..
Ifthe payment is a monthly payment; then the
compounding rate of return has to be a
monthly rate of return.
Example: A 15% ANNUAL rate of return is
equal to a monthly rate of return of 1.25%
15/12 = 1.25
30. Buying the same car with monthly
payments: Financial Calculator
PV = 6,000
I/Y = 1.25 [15/12]
N = 48 [4*12]
CPT PMT = $-166.98
31. Student loan payments
Guestimate your total
school loans…..(PVA)
How many years to
pay them off? (covert
to monthly payments)
At what interest rate?
R u consolidating?
32. Review:
Future value – the value, in the future, of
a current investment
Formula?
Rule of 72 – estimates how long your
investment will take to double at a given
rate of return
Present value – today’s value of an
investment received in the future
Formula?
33. Review (cont’d)
Annuity – a periodic series of equal
payments for a specific length of time
Future value of an annuity – the value, in
the future, of a current stream of
investments
Formula?
Present value of an annuity – today’s
value of a stream of investments
received in the future
Formula?
34. Review (cont’d)
Amortized loans – loans paid in equal
periodic installments for a specific length
of time