HP 17BII+: Actuary and Finance Formulas
Simple Interest
Simple Interest is different from compound interest. In simple interest, the interest is calculated only on the base principal amount, no matter how much time passes. In compound interest, the interest is calculated each period (typically monthly or annually) on both the amount of current principal and accumulated interest. The time value of money (TVM) keys on financial calculators deal work on compound interest.
The formula to calculate future value on a base amount (no annuity) based on simple interest is:
FV = PV * (1 + I%) * N
where the formula to calculate the future value on a base amount (no annuity) compound interest is:
FV = PV * (1 + I%)^N = PV * (1 + I%)N
HP 17BII+ formula:
SIMPLE: FV=PV×(1+0.01×I%×YEARS)
Note:
* The percent sign (%) is just a character in the HP 17B's solver.
* I% = periodic interest, YEARS = number of years
Example:
1. Find the future value of a 6% simple interest loan of $150.00. The loan last 90 days on a 365-day year.
PV = 150.00, I% = 6, YEARS = 90/365 (90 [÷] 365 [=] in ALG mode, 90 [ENTER] 365 [÷] in RPN mode)
Result: FV = 152.22
(Note that the cash flow convention is not followed here)
2. Find the simple interest rate if you made an auto business loan of $1,750.00 for 6 months (1/2 year) and received $1,790.00.
PV = 1,750.00, FV = 1,790.00, YEARS = 0.5
Result: I% = 4.90 (about 4.9%)
Ordinary Growing Annuity
The following formula calculates the present value of a growing annuity: with R% the interest rate of the annuity and G% the growth of each payment. Note that both R% and G% are both periodic rates.
For more information, along with a program for both the Swiss Micros DM42 and HP 71B, click here: http://edspi31415.blogspot.com/2021/01/swiss-micros-dm42-and-hp71b-present.html
HP 17BII+ formula:
GROWING: PV=PMT×∑(K:1:N:1:(1+.01×G%)^(K-1)÷(1+.01×R%)^K)
Examples:
1. Find the present value of a growing annuity with base payment of $1,000, if each payment grows 5% each period for 12 periods. The interest rate of the annuity is 4%.
PMT = 1,000.00, G% = 5, R% = 4, N = 12
Result: PV = 12,168.66
(Note that the cash flow convention is not followed here)
2. Same situation as Example 1 except the payment grows 3%.
PMT = 1,000.00, G% = 3, R% = 4, N = 12
Result: PV = 10,947.40
3. What is the required growth rate if the present value is $12,000.00?
PMT = 1,000.00, R% = 4, N = 12, PV = 12,000.00
Result: G% = 4.74 (4.73859628349) (after some time)
Present Value or Payment of a Annuity of Variable Interest Rate
This formula calculates the present value of an annuity of constant payment that varies in interest rate per period.
1. Create a SUMS list named LIST. This will be the list of each interest rate from Period 1 to Period N.
2. Go to the Solver, enter the required parameters (PMT or PV) and solve (for either PMT or PV).
HP 17BII+ formula:
PVVARI%: PV=PMT×∑(I:1:SIZES(LIST):1:(1+ITEM(LIST:1)×.01)^(-I))
Example:
What is the annual payment of a loan of $5,000.00 loan with a variable interest rate:
Years 1-3: 5.0%
Years 4-6: 4.0%
Year 7: 4.5%
LIST = {5, 5, 5, 4, 4, 4, 4.5}
PV = 5,000.00
Result: PMT = 843.86
Solve for Interest and Number of Periods Given Present Value Annuity Factor and Future Value Annuity Factor
Given the present value of annuity factor (PVAF) and the future value of annuity factor (FVAF), we can solve the periodic interest rate and number of periods are:
I% = (1/PVAF - 1/FVAF) * 100
N = ln(FVAF/PVAF) / ln(1 + I%*.01)
HP 17BII+ formula:
IF(S(I%):L(I:INV(PVAF)-INV(FVAF))×100-I%:LN(FVAF÷PVAF)÷LN(1+G(I))-N)
Solve for I% first, then for N.
Example:
PVAF = 12, FVAF = 18
Result: I% = 2.78, N = 14.8
You can find more information here: http://edspi31415.blogspot.com/2021/01/hp-12c-solving-two-actuarial-problems.html
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.
Note: This is the first post done with a Chromebook using the editor in both Blogger and Google Docs, and eventually make diagrams using Sketchpad or an applicable Google/Android app. For the better part of three years, I used Windows based application WordPad and Paint. I miss having a laptop, being able to visit favorite local coffee shops and being able to do work there. I can't wait until the world opens up again. Time's are a changing.
Special gratitude to all the nurses and doctors who have and continually to be on the front lines in the COVID-19 crisis.
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.
