Interest and Borrowing

Hong Kong

Stage 1 - Stage 3

Lesson

Credit cards are everywhere in today's society and used all around the world as a method of payment as they allow people to buy goods and services that may be too expensive to buy in a one-off purchase otherwise. Further, with online shopping becoming more common, you can also buy items from sellers in another country and pay for them more easily than, say, by converting currencies and posting the cash!

People who get credit cards from banks or a financial institutions are basically getting a loan. It is not a one-off loan for a specific item, such as a house, but rather a continuous line of credit where consumers are allowed to have a continuing balance of debt if they cannot repay the full balance.

However, banks have *terms*, or conditions, that specify your *credit limit* (i.e. how much you're allowed to spend) and how long you have to repay the money before they charge you *interest* (additional money as a fee for borrowing their money and not repaying it on time). Since the level of debt among teenagers is rising at an alarming rate, it is important that we understand how credit cards work and how interest is calculated because we don't want to end up in debt and have to repay a huge amount of money!

Balance: the total amount owing on a credit card.

Charges: purchases or expenses charged to a credit card.

Repayments: money paid back to the bank for any charges that may have been incurred.

Statement: a document generated by a bank or financial institution showing all transactions and the final account balance within a given period of time.

Per annum: each year.

The interest rate is normally written as a rate per annum. However, the interest may actually be charged daily, weekly, monthly etc. So how do we calculate the *equivalent interest rate* if we want to know what the rate being charged per day? Well, it's the same process as when we learnt to convert other rates. Since there are $365$365 days in a regular year, we would **divide** the annual interest rate by $365$365. Conversely, if we wanted to go from a daily rate to an annual rate, we would **multiply** by $365$365. The number you multiply of divide by will change depending on what units you are convert to and from.

Calculate the equivalent annual rate of interest when the monthly rate is $0.2%$0.2%. Write your answer as a percentage to $2$2 decimal places.

**Think:** There are $12$12 months in a year.

**Do:** $12\times0.2=2.4%$12×0.2=2.4% p.a.

Interest on credit card debt compounds. So to calculate the amount owing, including the interest incurred, we need to use the compound interest formula:

$A=P\left(1+r\right)^n$`A`=`P`(1+`r`)`n`

or, if we need to adjust the rate to match the time periods:

$A=P\left(1+\frac{r}{k}\right)^{nk}$`A`=`P`(1+`r``k`)`n``k`

**Remember:** The time period needs to be in equivalent units to the rate (i.e. both in terms of days, weeks, months etc).

The opening balance on a credit card is $\$1600$$1600 and purchases of $\$631$$631 and repayments of $\$419$$419 are made during the month. If the credit card company requires a minimum payment of $8%$8% of the closing balance, find the minimum payment required. Write your answer to the nearest cent.

**Think:** We need to work out the balance owing before we calculate the minimum payment.

**Do: **

Balance: $1600+631-419=\$1812$1600+631−419=$1812

Minimum payment: $1812\times8%=\$144.96$1812×8%=$144.96

The opening balance on a credit card is $\$1600$$1600, and purchases of $\$631$$631 and repayments of $\$419$$419 are made during the month.

If the credit card company requires a minimum payment of $8%$8% of the closing balance,

find the minimum payment required.

Write your answer to the nearest cent.