Financial applications and online calculators
Beyond using spreadsheets there are several options to explore compound interest investments and loans using technology known as Time-Value-Money solvers (TVM solvers) and there are many online versions which you can use to explore scenarios efficiently. 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.
There are also many online calculators which offer to calculate values for specific problems such as loan repayment calculators or compound investment comparison calculators.
The calculator applications and online TVM solvers 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/Y | number of payments per year |
| $C/Y$C/Y | number of compounding periods per year |
One point of difference between these solvers and the way we have been using the compound interest formula is 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.
You can use the following applet to explore the problems below:
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Worked example
Suppose $\$10000$$10000 is invested in an account earning interest at $6%$6% p.a. compounded quarterly. How much is in the account after $3$3 years?
Think: As we are compounding quarterly the number of compounding periods per year is $4$4, and so we set both $C/Y$C/Y and $P/Y$P/Y equal to $4$4. Then since the amount is invested for $3$3 years we have $N$N equal to $4\times3=12.$4×3=12. When solving a problem using a financial solver you should always write down the values you are entering into the calculator and indicate which value you are solving for.
Do:
| $N$N | $=$= | $4\times3=12$4×3=12 |
There are $4$4 quarters per year, and $3$3 years. |
| $I$I | $=$= | $6$6 |
Input as a percentage per annum. |
| $PV$PV | $=$= | $-10000$−10000 |
Negative because this is an investment - we are giving the bank money. |
| $PMT$PMT | $=$= | $0$0 |
No payments are mentioned. |
| $FV$FV | $=$= | ? |
This is the value we are trying to find. |
| $P/Y$P/Y | $=$= | $4$4 |
Set equal to $C/Y$C/Y, so that $N$N is equal to the number of compounds. |
| $C/Y$C/Y | $=$= | $4$4 |
Compounding quarterly: there are $4$4 quarters per year. |
Once you have entered all the known values you can tap or move the cursor (depending on your calculator) to the unknown and the calculated value will appear: $FV=11956.18$FV=11956.18
Finally, we should interpret the result: there will be $\$11956.18$$11956.18 in the account after $3$3 years.
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.