1.6 Calculating the Term
Learning Objectives
- Calculate the number of compounding periods
- Calculate the term of a loan or investment
Formula & Symbol Hub
Symbols Used
or = Effective interest rate = Future value or maturity value = Periodic interest rate or = Nominal interest rate per year or = Number of compounds per year or compounding frequency or = Total number of compound periods for the term = Present value of principal
Formulas Used
-
Formula 1.1 – Total Number of Compounds
-
Formula 1.2 – Periodic Interest Rate
-
Formula 1.3 – Future Value
-
Formula 1.4 – Present Value
Introduction
How long will it take to reach a financial goal? At a casual get-together at your house, a close friend discusses saving for a 14-day vacation to the Blue Bay Grand Esmeralda Resort in the Mayan Riviera of Mexico upon graduation. The estimated cost from Travelocity.ca is
Using a Financial Calculator
Although it is possible to find the number of compounding periods by using the future value or present value formulas, it is much more practical to use a financial calculator. You use the financial calculator in the same way as described previously, but the only difference is that the unknown quantity is
Using the TI BAII Plus Calculator to Find the Number of Compoundings for Compound Interest
Enter values for the known variables (
- For the main button keys in the TVM row (i.e.
, , , , ), enter the number first and then press the corresponding button.- For example, to enter
, enter on the calculator and then press N.
- For example, to enter
- For
and , press 2nd I/Y. At the screen, enter the value for and then press ENTER. Press the down arrow to access the screen. At the screen, enter the value for and then press ENTER. Press [latex]2nd QUIT (the CPT button) to exit the menu.- For example, to enter
and , press 2nd I/Y. At the screen, enter and press ENTER. Press the down arrow. At the screen, enter and press ENTER. Press 2nd QUIT to exit.
- For example, to enter
After all of the known quantities are loaded into the calculator, press CPT and then
Things to Watch Out For
When entering both
Example 1.6.2
Jenning Holdings invested
Solution
Step 1: Calculate the value of
N | ? |
PV | |
FV | |
PMT | |
I/Y | |
P/Y | |
C/Y |
Step 2: Convert
Step 3: Write as a statement.
Jenning Holdings has had the money invested for six years and nine months.
Example 1.5.3
Tabitha estimates that she will need at least
Solution
The timeline for the investment is shown below.

Image Description
The image shows a horizontal, light blue line representing a loan timeline with labels corresponding to values discussed in the rest of the example.
Step 1: Calculate the value of
N | ? |
PV | |
FV | |
PMT | |
I/Y | |
P/Y | |
C/Y |
Step 2: Convert
Step 3: Write as a statement.
If Tabitha invests the
Try It
1) You just took over another financial adviser's account. A client invested
Solution
N | ? |
PV | |
FV | |
PMT | |
I/Y | |
P/Y | |
C/Y |
The money has been invested for
Section 1.6 Exercises
- How long will it take an investment of
to mature to at least if the interest rate is compounded monthly?
Solution
years, months - What is the term of an investment of
that has a maturity value of at compounded quarterly?
Solution
years, months - How long did it take a
investment to earn in interest if the interest rate is compounded semi-annually?
Solution
years, months - A debt of
is owed. Suppose prevailing interest rates are compounded quarterly. How far in advance was the debt paid if the creditor accepted a payment of ?
Solution
years, months - Wayne was late in making a
payment to Dora. If Dora accepted a payment of and charged compounded semi-annually, how late was the payment?
Solution
year, months - How long will it take
to become at compounded quarterly?
Solution
years, months - A friend of yours just won the
/ category on the Lotto Max (matching six out of seven numbers), and her share of the prize was . She wants to pay cash for a new home that sells for . If she can invest the money at compounded semi-annually, how long will she have to wait to purchase the home assuming its sale price remains the same?
Solution
years, months - Lakewood Properties anticipates that the City of Edmonton in the future will release some land for a development that costs
million. If Lakewood can invest million today at compounded monthly, how long will it take before it will have enough money to purchase the land?
Solution
years, months - As marketing manager, you want to pursue a new product development for which you require
million for research. However, budgetary constraints mean you can only receive . If you take your budget and invest it at compounded monthly, how long will it be before you can pursue the necessary research for the project?
Solution
year, months - How long will it take money to triple if it earns
compounded quarterly?
Solution
years, months
Attribution
"1.6 Calculating the Term" from Financial Math - Math 1175 by Margaret Dancy is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.