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

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

Answer 2

Answer:

$8,358.72

Step-by-step explanation:

We know the formula for the compound interest given by,

$A=P \times (1+\frac{r}{n})^{nt}$, 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.

$A=2600 \times (1+\frac{0.043}{12})^{5 \times 12}$

i.e. $A=2600 \times (\frac{12.043}{12})^{60}$

i.e. $A=2600 \times (\frac{12.043}{12})^{60}$

i.e. $A=2600 \times (1.0036)^{60}$

i.e. $A=2600 \times 1.2406$

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,

$A=3225.56 \times (1+\frac{0.137}{12})^{7 \times 12}$

i.e. $A=3225.56 \times (\frac{12.137}{12})^{84}$

i.e. $A=3225.56 \times (1.0114)^{84}$

i.e. $A=3225.56 \times 2.5914$

i.e. $A=8,358.72$

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