fx-3900PV Programs: Finance Factors

fx-3900PV Programs: Finance Factors

I’m revisiting the fx-3900Pv, which seems to be a hit. The last set of programs from May 3 of this year: https://edspi31415.blogspot.com/2025/05/casio-fx-3900pv-linear-system-poisson.html

Remember: When using the ENT (enter/input) command, we must enter a valid number and then the next step. The number that precedes ENT is not counted as a step and is not recorded.

Example: x + 9

In LRN (learn) mode (Mode EXP):

ENT (enter any number)

+

9

=

Casio fx-3900Pv: Simple Interest

maturity amount = principal amount * (1 + 0.01 * I%) * N ÷ 360

interest accrued = maturity amount – principal amount

I% = annual interest rate

N = number of days

The Act/360 method is used.

Code (23 steps):

ENT # enter principal amount (PV)

Kin 1

×

(

1

+

.

0

1

×

ENT # enter interest rate

×

ENT # enter number of days

÷

3

6

0

)

=

HLT # pause, display maturity amount

-

Kout 1

= # display interest accrued, end program

Example 1:

Inputs:

Principal Amount: 1,000.00

Rate: 5%

Number of Days: 30

Output (rounded to 2 decimal places)

Maturity Amount: 1,004.17

Interest Accrued: 4.17

Example 2:

Inputs:

Principal Amount: 360.00

Rate: 8%

Number of Days: 90

Output (rounded to 2 decimal places)

Maturity Amount: 367.20

Interest Accrued: 7.20

Casio fx-3900Pv: Compound Interest Factor with Compounding Periods

The following program calculates the compound interest factor:

factor = (1 + I% ÷ PYR) ^ (YRS × PVR)

where

I% = annual interest rate

PYR = payments per year (compounding periods)

YRS = number of years (N)

The factor is used in simple compound interest problems:

FV = PV × factor

where:

FV = future value

PV = present value

Code (19 steps):

(

1

+

.

0

1

×

ENT # enter interest rate

÷

ENT # enter payments per year

Kin 1

)

x^y

(

ENT # enter number of years

×

Kout 1

)

=

Example:

Find the compound interest interest factor for: I% = 5%, 12 payments a year, 4 years

Factor: 1.220895351

If an investor expects a $5,000.00 payoff, what should the investor pay?

PV = FV ÷ X

Keys: (with the answer from program displayed: [ 1/x ] [ × ] 5000 [ = ])

PV (rounded): 4,0953.36

Casio fx-3900Pv: Loan Annuity Factor

The following program calculates the loan annuity factor:

factor = ( ( 1 - ( 1 + I% ÷ PYR ) ^ (-YRS × PYR) ) ÷ ( I% ÷ PYR )

where

I% = annual interest rate

PYR = payments per year (compounding periods)

YRS = number of years (N)

The factor is used in loan problems without balloon payments, and assume that the payments occur at the end of each period (ordinary annuity):

PV = PMT × factor

where:

PV = present value

PMT = periodical payments

Code (30 steps):

ENT # enter interest rate

÷

ENT # enter payments per year

Kin 2

×

.

0

1

=

Kin 1 # K1 = I% ÷ PYR

ENT # enter number of years

×

Kout 2

=

Kin 2 # K2 = YRS × PYR = N

(

1

-

(

1

+

Kout 1

)

x^y

Kout 2

+/-

)

÷

Kout 1

=

Example:

A student buys a car at $35,619 (after taxes and fees). The student gets a six year loan at 5.7% and pays at the end of each month. What is the payment?

PMT = PV ÷ factor

where PV = 35619, I% = 5.7, PYR = 12 (monthly payments), YRS = 6

Running the program with inputs 5.7, 12, 6: 60.85819003

Payment: [ 1/x ] [ × ] 35619 [ = ]: 585.28 (rounded)

Casio fx-3900Pv: Sinking Fund Factor (Savings Account)

The following program calculates the sinking factor (used for savings accounts):

factor = ( (1 + I% ÷ PYR) ^ (YRS × PYR) – 1 ) ÷ (I% ÷ PYR)

The factor is used in determining the future value of savings plans with regular deposits made at the end of each period:

FV = PMT × factor

Code (29 steps):

ENT # enter interest rate

÷

ENT # enter payments per year

Kin 2

×

.

0

1

=

Kin 1 # K1 = I% ÷ PYR

ENT # enter the number years

×

Kout 2

=

Kin 2 # K2 = YRS × PYR

(

(

1

+

Kout 1

)

x^y

Kout 2

-

1

)

÷

Kout 1

=

Example:

A child’s parents opens up an account on the child’s first birthday. The parents contribute $200.00 per month for the next 18 years. The account pays a fixed rate of 3% per month. What is the value of the fund when the child turns 18?

Note: The account is opened on the child’s first birthday, hence 17 years pass.

FV = PMT × factor

where PMT = 100, I% = 3, PYR = 12, YRS = 17

Running the program with inputs 3, 12, 17: 265.69267

Future Value: [ × ] 200 [ = ]: 53,138.54 (rounded)

Until next time, stay safe and sane,

Eddie

All original content copyright, © 2011-2025. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.

The content on this blog is 100% generated by humans. The author does not use AI engines and never will.

Annuity Due in Terms of Ordinary Annuity

Annuity Due in Terms of Ordinary Annuity

Annuity:  Ordinary vs. Due

The distinction is determined when the first payment is made:

Ordinary Annuity:   the first payment is made at the end of the first period, with no payment made at the beginning (period 0) of the annuity. 

Annuity Due:  the first payment is made at the very beginning of the annuity, with no payment made at the end of the annuity.  

For today's exercise, assume all payments in annuity are all equal.  To simplify, I am going to set payments to 1 monetary unit (Dollars, Euros, Lira, Yen, etc).

Present Value

The present value of an annuity is today's value of the annuity, with future payments and cash flows are discounted back to today using the periodic interest rate.  On financial calculators, the present value is symbolized by the PV key.  

Let i be the interest rate of the annuity, in decimal format.  

Example, for 5% periodic rate, i=0.05.

Let v = 1/(1 + i).   

Present Value of an Ordinary Annuity

Given the payment of 1 monetary unit, an annuity of n periods, equally spaced out, and interest rate i, the present value of this ordinary annuity is the sum:

PVAF = v + v^2 + v^3 + ... + v^(n-1) + v^n = Σ(v^x for x=1 to n)

The above is known as the present value annuity factor, or PVAF.  

A closed formula for PVAF is:

PVAF = (1 - (1 + i)^-n) / i

Present Value of an Annuity Due

Likewise, the present value of the annuity due is the sum:

PVAFD = 1 + v + v^2 + v^3 + ... + v^(n-1) = Σ(v^x for x=0 to n-1)

A closed formula for PVAFD is:

PVAFD = (1 - (1 + i)^-n) / (1 - 1/(1 + i))

We can express PVAFD in terms of PVAF by:

PVAFD = 1 + v + v^2 + v^3 + ... + v^(n-1)

PVAFD + v^n = 1 + v + v^2 + v^3 + ... + v^(n-1) + v^n

PAVFD + v^n = 1 + PVAF

PAVFD = 1 + PVAF - v^n

PAVFD = 1 + (1 - (1 + i)^-n) / i - (1 + i)^-n

Example:  i = 0.04, n = 36

PAVFD = 1 + (1 - 1.04^-36) / 0.04 - 1.04^-36 ≈ 19.6646

This is the same as setting up TVM (time value of money) keys on most financial calculators or any calculator with a TVM solver as:

n = 36, I = 4, PMT = -1, FV = 0, (if needed, P/Y = 1),  BEGIN mode

Solve for PV:  19.6646...

Future Value

The future value of an annuity is the final value of the annuity, including the accumulated interest of payments and cash flows from the date the payment to the end of the annuity.  On financial calculators, the future value is symbolized by the FV key.  

Let w = 1 + i

Future Value of an Ordinary Annuity

Given the payment of 1 monetary unit, an annuity of n periods, equally spaced out, and interest rate i, the future value of this ordinary annuity is the sum:

FVAF = 1 + w + ... + w^(n-3) + w^(n-2) + w^(n-1) = Σ(w^x for x=0 to n-1)

The above is known as the future value annuity factor, or FVAR.  

A closed formula for FVAF is:

FVAF = ( (1 + i)^n - 1 ) / i

Future Value of an Annuity Due

Likewise, the future value of the annuity due is the sum:

FVAFD = w + ... + w^(n-3) + w^(n-2) + w^(n-1) + w^n = Σ(w^x for x=1 to n)

A closed formula for FVAFD is:

FVAFD = (1 + i) * ( (1 + i)^n - 1 ) / i 

We can express FVAFD in terms of FVAF by:

FAVFD = w + ... + w^(n-3) + w^(n-2) + w^(n-1) + w^n 

1 + FAVFD = 1 + w + ... + w^(n-3) + w^(n-2) + w^(n-1) + w^n 

1 + FAVFD = FAVD + w^n

FAVFD = FAVD + w^n - 1

FAVFD = ( (1 + i)^n - 1 ) / i + (1 + i)^n - 1

Example:  i = 0.04, n = 36

FAVFD = (1.04^36 - 1) / 0.04 + 1.04^36 - 1 ≈ 80.7022

Using the TVM keys or solver:

n = 36, I = 4, PMT = -1, PV = 0, (if needed, P/Y = 1),  BEGIN mode

Solve for FV:  80.7022...

On tomorrow's blog, January 24, I will cover two actuarial problems. 

Source:

Finan, Marcel B.  A Basic Course in the Theory of Interest and Derivatives Markets:  A Preparation for the Actuarial Exam FM/2   Arkansas Tech University, 2017.  

Eddie

All original content copyright, © 2011-2021.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.