# I have four questions, all of which I have no idea how to setup the problem. Any help is appreciated. 1. Assume that you have a balance of $3000 on your American Express credit card and that you...

I have four questions, all of which I have no idea how to setup the problem. Any help is appreciated.

1. Assume that you have a balance of $3000 on your American Express credit card and that you make no more charges. If your APR is 18% and each month you make only the minimum payment of 4% of your balance, then the formula for the balance after *t* monthly payments is given by 3000(0.9744)*t *. What will the balance be after 20 months?

**A.**$1785.94

**B.**$980.10

**C.**$1609.96

**D.**$4858.62

2. You have a balance of $12,000 for your tuition on your credit card and you make no further charges. If your APR is 16.7% and each month you make only the minimum payment of 2% of your balance, then find a formula for the balance after *t* monthly payments.

**A.**12,000(0.966362)

*t*

**B.**12,000(0.993638)

*t*

**C.**12,000(1.0342)

*t*

**D.**12,000(1.00581)

*t*

3. Assume that you have a balance of $5000 on your Visa credit card and that you make no more charges. If your APR is 22% and each month you make only the minimum payment of 3% of your balance, then find a formula for the balance after *t* monthly payments.

**A.**5000(0.987783)

*t*

**B.**5000(1.048883)

*t*

**C.**5000(1.011117)

*t*

**D.**5000(0.952217)

*t*

4. Suppose the stock of Microsoft increases in value by $5 per share. If all other Dow stock prices remain unchanged, how does this affect the DJIA?

**A.**37.80 points up

**B.**30.24 points up

**C.**22.68 points up

**D.**15.12 points up

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### 1 Answer

(1) We are given the formula for the amount owed after `t ` months is `"balance"=3000(.9744)^t `

Since t=20 we have a balance of `3000(.9744)^(20)~~1785.939573 `

So the correct answer is (a).

(2) We have a debt of $12,000 with an APR of 16.7% and a minimum payment of 2% of the balance.

Each month we are charged `.167/12~~.0139166667 ` percent. The APR is the annualized percent, so we divide by 12 to find the monthly rate. (Note that this is the APR not the APY.) The balance before the payment is found by multiplying the last month's balance by 1.0139166667. (This uses the distributive property -- the new balance will be the old balance plus the additional interest, so the new balance = old balance plus old balance times .0139166667 or new balance = old balance times 1.013966667)

To find this months balance after payment, we multiply the balance plus interest by .98. (Again we use the distributive property -- the payment reduces the balance by 2% so we take bal-bal*.02=.98 bal)

So each month we are taking the previous balance times 1.013916667 times .98 or previous balance times .993638.

The formula is `12000(.993638)^t ` for a correct answer of (b)

(3) Using the same reasoning as (2) we get a formula `5000(.987783)^t ` , so the correct answer is (a)

(4) To determine the change in the Dow Jones index for a change in price of a stock you sum the values and divide by the Dow divisor which is currently .15571590501117. A $1 change in the sum of the values yields a `1/.1557159~~6.42 ` change in the index, so a $5 change should yield a 32.11 change in the index. As this is not one of the answers provided, the problem must date from a previous divisor. You will need to check the course materials/text to find the Dow divisor being used to get the correct answer.

**Sources:**