Interest problem

**NEMO** · May 23rd 2008, 06:23 AM

Suppose you owe $1000 on your credit card and that at the end of each month an additional 1.4708% of the amount you owe is added on the amount you owe (this is what would happen if your credit card charged an annual percentage rate of 17.6490%) Lets assume that you do not pay off any of this debit or the interest that is added to it. Lets also assume that you dont add on any more debt other that the interest charged.

How much will you owe after 6 months? after one year? after 2 years/

Calculate (1.014708)48 and notice that this number is ust a little larger than 2. Based o this calculation, what will happen to your debt every 4 years Explain?

Suppose you didnt pay off your debt for 40 years. Using part b determine approximatley how much you owe?

Its long but its an MCAS exam practaice question.

**janvdl** · May 23rd 2008, 07:02 AM

Originally Posted by NEMO

Suppose you owe $1000 on your credit card and that at the end of each month an additional 1.4708% of the amount you owe is added on the amount you owe (this is what would happen if your credit card charged an annual percentage rate of 17.6490%) Lets assume that you do not pay off any of this debit or the interest that is added to it. Lets also assume that you dont add on any more debt other that the interest charged.

How much will you owe after 6 months? after one year? after 2 years/

6 months:
$A = (1000) \left(1 + \frac{1.4708}{100} \right)^{6}$

One year:
$A = (1000) \left(1 + \frac{1.4708}{100} \right)^{12}$

Two years:
$A = (1000) \left(1 + \frac{1.4708}{100} \right)^{24}$

Originally Posted by NEMO

Calculate (1.014708)48 and notice that this number is ust a little larger than 2. Based o this calculation, what will happen to your debt every 4 years Explain?

Notice that 1.014708 represents the value for the part in brackets in the above expressions. $( \ 1 + \frac{1.4708}{100} \ )$

(1000) is the original amount.

So every four years the amount you owe will double.

Originally Posted by NEMO

Suppose you didnt pay off your debt for 40 years. Using part b determine approximatley how much you owe?

The amount will be approximately 1024, in other words $2^{10}$ , times larger than at the beginning.
(Thanks Earboth.)

**NEMO** · May 23rd 2008, 07:07 AM

Thank you very much

**janvdl** · May 23rd 2008, 07:11 AM

Originally Posted by NEMO

Thank you very much

You are welcome

**phaneendra11** · May 23rd 2008, 07:18 AM

Originally Posted by NEMO

Suppose you owe $1000 on your credit card and that at the end of each month an additional 1.4708% of the amount you owe is added on the amount you owe (this is what would happen if your credit card charged an annual percentage rate of 17.6490%) Lets assume that you do not pay off any of this debit or the interest that is added to it. Lets also assume that you dont add on any more debt other that the interest charged.

How much will you owe after 6 months? after one year? after 2 years/

Calculate (1.014708)48 and notice that this number is ust a little larger than 2. Based o this calculation, what will happen to your debt every 4 years Explain?

Suppose you didnt pay off your debt for 40 years. Using part b determine approximatley how much you owe?

Its long but its an MCAS exam practaice question.

Hi I will help you soon. I am working on it.

**janvdl** · May 23rd 2008, 07:19 AM

Originally Posted by phaneendra11

Hi I will help you soon. I am working on it.

You will notice it has been solved.

**earboth** · May 23rd 2008, 07:20 AM

Originally Posted by janvdl

...

So every four years the amount you owe will double.

The amount will be 20 times larger than at the beginning. (This is quite an approximation...)

Hi, JanvdL,

I don't want to pick at you but you see me quite confused:

During 40 years every 4 years the actual amount of money will double. That means you have 10 "doublings". wouldn't that be

$A(40)=A(0)\cdot 2^{10}$

So the original amount is enlarged bei approximately factor 1000.

Or did I misunderstand the question completely?

**janvdl** · May 23rd 2008, 07:24 AM

Originally Posted by earboth

Hi, JanvdL,

I don't want to pick at you but you see me quite confused:

During 40 years every 4 years the actual amount of money will double. That means you have 10 "doublings". wouldn't that be

$A(40)=A(0)\cdot 2^{10}$

So the original amount is enlarged bei approximately factor 1000.

Or did I misunderstand the question completely?

You are very correct. Thank you.

**colby2152** · May 23rd 2008, 07:32 AM

It seems as if there is quite a bit of confusion over this question. Let me try and help you out!

Originally Posted by NEMO

Suppose you owe $1000 on your credit card and that at the end of each month an additional 1.4708% of the amount you owe is added on the amount you owe (this is what would happen if your credit card charged an annual percentage rate of 17.6490%) Lets assume that you do not pay off any of this debit or the interest that is added to it. Lets also assume that you dont add on any more debt other that the interest charged.

How much will you owe after 6 months? after one year? after 2 years/

$A(t)=1000*1.014708^t$ where t is # of months

Solve for $A(6), A(12), A(24)$

Originally Posted by NEMO

Calculate (1.014708)48 and notice that this number is ust a little larger than 2. Based on this calculation, what will happen to your debt every 4 years Explain?

Every four years, the amount on the loan should be doubled, approximately - note that $1.014708^{48} = 2.01545 \ne 2$

Originally Posted by NEMO

Suppose you didnt pay off your debt for 40 years. Using part b determine approximatley how much you owe?

If you're not making any payments, then this original amount is accruing at 1.4708% interest monthly for 40 years. Approximately, it should have doubled 10 times and be a bit over $2^{10} * 1000 = 1,024,000$ . Let us solve for T = 40 years

$T = 40$ years

$t = 12T$

$t = 480$ months

$A(480) = 1000*1.014708^{480} \Rightarrow 1,105,911.83$

Note that $1,105,911.83 > 1,024,000$

The percent error in our approximation was: $\frac{1105911.83}{1024000} - 1 = 0.079992021$

That is an 8% error! This is why actual calculations are important, especially if you are planning on becoming an actuary...

Originally Posted by NEMO

Its long but its an MCAS exam practaice question.

CAS is the Casualty Actuarial Society, and their exams are numbered with Exam 3 being split between Financial Economics and Life Contingencies. What is exam MCAS?

If you are an actuarial student, and it looks as if you are, then you may be inclined to take a look at a new actuarial forum started by MHF members: Actuarial Community

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