Question

Sandra has two credit cards, P and Q. Card P has a balance of $726.19 and an interest rate of 10.19%, compounded semiannually. Card Q has a balance of $855.20 and an interest rate of 8.63%, compounded monthly. Assuming that Sandra makes no purchases and no payments with either card, after four years, which card’s balance will have increased by more, and how much greater will that increase be?

Answer 1

Answer: C

Step-by-step explanation:

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Answer 2

Ans.

a) Card P would have increased more, 48.82% in terms of its initial balance.

b) Card P would have increase by 7.77% more when compared to Card Q.

Step-by-step explanation:

Hi, first, we need to find the balance after 4 years for both, Card P and Card Q and then we need to check how much its final balance grew in terms of the initial balance. In order to find the final balance of both cards, we have to convert all those compounded rates into effective rates. This is how.

`r(CardP)=(0.1019)/(2) =0.05095`

So the equivalent rate for card P is 5.095% effective semi-annually, and since this rate is presented in terms of semesters, the number to be use to find the final balance is 4 years * 2 semesters/year= 8 semesters.

For card D

`r(CardP)=(0.0863)/(12) =0.00719167`

So the equivalent rate for card D is 0.719167% effective monthly, and since this rate is presented in terms of months, the number to be use to find the final balance is 4 years * 12 months/year= 48 months.

With that in mind, the final balance of card P is:

`FinalBalance(P)=726.19(1+0.05095)^(8) =1,080.85`

And the final balance of card Q is:

`FinalBalance(Q)=855.20(1+0.00719167)^(48) =1,206.28`

Now, we have to find how much each initial balance grew in terms of each initial balance.

`growth=((FinalBalance-InitialBalance))/(InitialBalance)`

`growth(P)=((1080.85-726.29))/(726.29) =0.4882`

`growth(Q)=((1206.28-855.20))/(855.20) =0.4105`

So card P grew 48.82% in terms o its initial balance and card Q grew 41.05% in terms or its initial balance, therefore, the card balance thar grew the most was card P and it did it by 7.77% (48.82% - 41.05% = 7.7%).

Best of luck.