Question

Olive transferred a balance of $2600 to a new credit card at the beginning of the year. The card offered an introductory APR of 4.3% for the first 5 months and a standard APR of 13.7% thereafter. If the card compounds interest monthly, what will Olives balance be at the end of the year?

Answer 1

$8,358.72

Explanation:

We know the formula for the compound interest given by,

`A=P * (1+(r)/(n))^(nt)`, where P = principle amount, r = rate of interest, n = number of times interest is compounded and t = time period.

It is given that he principle amount at the start of the year is $2600 and for the first 5 months, the rate of interest is 4.3% i.e. 0.043.

Moreover, the credit card is compounded monthly.

`A=2600 * (1+(0.043)/(12))^(5 * 12)`

i.e.
`A=2600 * ((12.043)/(12))^(60)`

i.e.
`A=2600 * ((12.043)/(12))^(60)`

i.e.
`A=2600 * (1.0036)^(60)`

i.e.
`A=2600 * 1.2406`

i.e.
`A=3,225.56`

Therefore, the principle amount at the start of the 6th month is $3,225.56 and for the next ( 12-5 ) = 7 months, the rate of interest is 13.7% i.e. 0.137.

So, the amount compounded monthly for the next few months is,

`A=3225.56 * (1+(0.137)/(12))^(7 * 12)`

i.e.
`A=3225.56 * ((12.137)/(12))^(84)`

i.e.
`A=3225.56 * (1.0114)^(84)`

i.e.
`A=3225.56 * 2.5914`

i.e.
`A=8,358.72`

Hence, we get that Olive's balance at the end of the year is $8,358.72.

Answer 2

Balance after five months

`2600(1+0.043)^(5)=3209.19`

At the beginning of the sixth month, the balance is $3209.19
The balance after the 12 months

`3209.19(1+0.137)^(7)=7883.48`

The balance at the end of the year is $7883.48