Most graphics and CAS calculators come with a built-in financial application which can be used to solve problems involving compound interest. These applications simply require you to enter in the known quantities (such as principal, interest, and number of compounding periods per year), and then the compound interest formula is applied or rearranged in the background to calculate the desired unknown quantity.
These financial applications typically use the following notation:
| $N$N | total number of payments |
| $I%$I% | interest rate as a percentage per annum |
| $PV$PV | the present value, or the principal |
| $PMT$PMT | the value of any additional regular payment |
| $FV$FV | the future value, or the final amount |
| $P/Y$P/Yor $PpY$PpY | number of payments per year |
| $C/Y$C/Y or $CpY$CpY | number of compounding periods per year |
Remember that if you enter a positive value for $PV$PV then the solver will return a negative value for $FV$FV. This corresponds to borrowing: when you borrow you have a positive present value (the bank gives you money) but in the future you owe money to the bank, which is what the negative number represents. Conversely if you enter a negative number for $PV$PV then the solver returns a positive $FV$FV - this corresponds to investing.
- Borrowing money - the bank is giving you money - use positive value for $PV$PV
- Investing money - you are giving your money to the bank - use negative value for $PV$PV
Another difference is that the solvers are set up to deal with regular payments in addition to the accumulation of interest. If there is no payment then we set $PMT$PMT to $0$0. We also set $P/Y=C/Y$P/Y=C/Y (the number of compounds per year) and then $N$N (number of payments of zero) is equal to the total number of compounding periods.
Worked example
Example 1
Suppose $\$10000$$10000 is invested in an account earning interest at $6%$6% p.a. compounded quarterly. How much is in the account after $3$3 years?
Note that since we are compounding quarterly the number of compounding periods per year is $4$4, and so we set both $C/Y$C/Y and $P/Y$P/Y equal to $4$4. Then since the amount is invested for $3$3 years we have $N$N equal to $4\times3=12.$4×3=12. When solving a problem using a financial solver you should always write down the values you are entering into the calculator and indicate which value you are solving for:
| $N$N | $=$= | $4\times3=12$4×3=12 |
There are $4$4 quarters per year, and $3$3 years. |
| $I$I | $=$= | $6$6 |
Input as a percentage per annum. |
| $PV$PV | $=$= | $-10000$−10000 |
Negative because this is an investment - we are giving the bank money. |
| $PMT$PMT | $=$= | $0$0 |
No payments are mentioned. |
| $FV$FV | $=$= | ? |
This is the value we are trying to find. |
| $P/Y$P/Y | $=$= | $4$4 |
Set equal to $C/Y$C/Y, so that $N$N is equal to the number of compounds. |
| $C/Y$C/Y | $=$= | $4$4 |
Compounding quarterly: there are $4$4 quarters per year. |
Once you have entered all the known values you can tap or move the cursor (depending on your calculator) to the unknown and the calculated value will appear: $FV=11956.18$FV=11956.18
Finally, we should interpret the result: there will be $\$11956.18$$11956.18 in the account after $3$3 years.
Select the brand of calculator you use below to view how the financial application appears in your calculator.
Casio Classpad
How to use the CASIO Classpad to complete the following tasks using the inbuilt financial solver.
Consider an investment of $\$2000$$2000 at $5%$5% p.a. compounded monthly.
Give your answers to two decimal places.
Find the value of the investment after $4$4 years.
Find the time required to earn $\$600$$600 in interest.
What rate would be required to reach a savings goal of $\$2600$$2600 within $4$4 years?
TI Nspire
How to use the TI Nspire to complete the following tasks using the inbuilt financial solver.
Consider an investment of $\$2000$$2000 at $5%$5% p.a. compounded monthly.
Give your answers to two decimal places.
Find the value of the investment after $4$4 years.
Find the time required to earn $\$600$$600 in interest.
What rate would be required to reach a savings goal of $\$2600$$2600 within $4$4 years?
Practice questions
Question 1
$\$13000$$13000 is borrowed at an interest rate of $2.5%$2.5% p.a. compounded semi-annually. Find how much is owed after $3.5$3.5 years in dollars.
Round your answer to the nearest cent.
Question 2
Nadia borrows $\$12000$$12000 at an interest rate of $3.5%$3.5% p.a. compounded weekly. If she makes no repayments, find the amount of interest that is owed after $3$3 years in dollars.
Assume there are $52$52 weeks in a year.
Round your answer to the nearest cent.
Question 3
Neil invests $\$900$$900 in a term deposit with a rate of $2.3%$2.3% p.a. compounded daily. How many years will it take for the investment to at least double in value?
Assume there are $365$365 days in a year.
Reducing balance loans using a financial application
Often it's more convenient to analyse various situations for a reducible balance loan using the financial facility of our calculator. Remember that the present value will be the value of the loan and is entered as a positive value, as the lender is receiving money from the bank. The payments will be negative as these are paid to the bank.
Worked example
example 2
Audrey takes out a car loan for $\$24000$$24000. The finance company charge her $8.5%$8.5% interest compounded monthly.
How much should Audrey repay each month if she wants to repay this loan in $5$5 years?
Using the financial application on our calculator we enter the details as follows:
| Compound Interest | ||
|---|---|---|
| N | $60$60 | There are $12$12 months per year, and $5$5 years. |
| I% | $8.5$8.5 | The annual interest rate |
| PV | $24000$24000 | PV is positive as the bank is giving Audrey money |
| PMT | This is the value we are trying to find. | |
| FV | $0$0 | The future balance will be zero. |
| P/Y | $12$12 | $12$12 payments per year |
| C/Y | $12$12 | Compounding monthly |
Solving we get: PMT = $-492.40$−492.40
So Audrey should pay $\$492.40$$492.40 each month.
Note: PMT displays as a negative number since the payments will be made from Audrey to the financial institution.
Practice question
Question 4
Mr and Mrs Gwen held a mortgage for $25$25 years. Over that time they made monthly repayments of $\$4500$$4500 and were charge a fixed interest rate of $4.4%$4.4% per annum, compounded monthly.
We will use the financial solver on your CAS calculator to determine how much they initially borrowed.
Which variable on the CAS calculator do we want to solve for?
PVAI%BNCPmtDFVEFill in the value for each of the following:
N:$\editable{}$I%:$\editable{}$Pmt:$\editable{}$FV:$\editable{}$PpY:$\editable{}$CpY:$\editable{}$Hence, state how much Mr. and Mrs. Gwen initially borrowed, correct to the nearest dollar.
What if number of payments $\ne$≠ number of compounding periods?
In real life, banks usually calculate interest on loan accounts monthly but people can choose to make fortnightly or even weekly repayments.
When the number of payments is not equal to the number of compounding periods the financial application of the calculator is a great tool.
N is the total number of payments $=\text{payments per year}\times\text{number of years}$=payments per year×number of years
P/Y is number of payments per year
C/Y is the number of times interest is calculated per year
Select the brand of calculator you use below to work through an example involving a reduce balance loan with differing payment and compound periods.
Casio Classpad
How to use the CASIO Classpad to complete the following tasks involving a reducing balance loan using the inbuilt financial solver.
A couple borrow $\$550000$$550000 to buy a house. The bank offers a reducing balance loan with an interest rate of $2.85%$2.85% p.a. compounded monthly. The couple opt to make fortnightly payments of $\$1200$$1200 in order to pay off the loan.
Assume there are $26$26 fortnights in a year.
Find the balance of the loan after two years.
How many years will it take the couple to pay off the loan? (Round your solution to one decimal place.)
TI Nspire
How to use the TI Nspire to complete the following tasks involving a reducing balance loan using the inbuilt financial solver.
A couple borrow $\$550000$$550000 to buy a house. The bank offers a reducing balance loan with an interest rate of $2.85%$2.85% p.a. compounded monthly. The couple opt to make fortnightly payments of $\$1200$$1200 in order to pay off the loan.
Assume there are $26$26 fortnights in a year.
Find the balance of the loan after two years.
How many years will it take the couple to pay off the loan? (Round your solution to one decimal place.)
Practice question
Question 5
Valerie borrows $\$345000$$345000 to buy an apartment. The bank offers a reducing balance loan with an interest rate of $2.35%$2.35% p.a. compounded monthly. Valerie opts to make fortnightly payments of $\$1250$$1250 in order to pay off the loan. Use the financial application on your calculator to answer the following questions.
Assume there are $26$26 fortnights in a year.
What is the balance, in dollars, after $100$100 weeks?
Round your answer to the nearest cent.
Approximate how long it takes her to pay off the loan in years.
Round your answer to two decimal places.