# Math Help - interset

1. ## interset

You take a loan with 5,25 % INTREST. The loan is payed in 10 years with a annual payment of 2500e. After 5 years the loan intrest was rised with 2,5%. How much must the annual poayment be raised to pay the loan in the planned 10 years???

2. I believe you are asking how much will the loan rise after the raise in interest? If so then
x=loan now*%rise/100

Should be easy for you to work out now.

3. Originally Posted by Rambo
You take a loan with 5,25 % INTREST. The loan is fully payed in 10 years with a annual payment of 2500e. After 5 years the loan intrest was rised with 2,5%. How much must the annual payment be raised to pay the loan in the planned 10 years???
I want to know how much more you should pay when the loan intrest rised after 5 years to still get the loan payed in 10 years time.

Not how tally suggested!

Can anyone calculate?

the answer is 174,82 but i dont know how to get to it....

5. I'm confused at what you mean by rised 2.5%? is the new interest rate 2.5% or 7.5%?

That being said, we can do 2/3 of the problem before you answer. Here is how you start:

We need the actual loan amount, for that, we need the present Value:

Annuity Immediate Present Value

Calculate Present Value, 5.25 for interest, 2500 for payment, 10 for term and press calculate. PV = 19,072.10 at time 5 after the 5th payment.

The formula for outstanding balance on a standard amortization loan is:

Outstanding Balance at time t = Payment * (1 - v^(n-t))/i where v = 1/(1+i). Plugging and chugging with all this business, we get:
v = 1/(1.0525) = .950119.
Balance at time 5 = 2500 * (1-0.950119^(10-5))/.0525 = 2500 * (1-.774265)/.0525 = 10,749.30

Now, when you answer my initial question, you will go to the initial link I gave you, and this time, press Calculate Payment. Enter new interest rate, time is now 5, and your Present Value is now 10749.30.

Make sense?

6. Originally Posted by mathceleb
I'm confused at what you mean by rised 2.5%? is the new interest rate 2.5% or 7.5%?

That being said, we can do 2/3 of the problem before you answer. Here is how you start:

We need the actual loan amount, for that, we need the present Value:

Annuity Immediate Present Value

Calculate Present Value, 5.25 for interest, 2500 for payment, 10 for term and press calculate. PV = 19,072.10 at time 5 after the 5th payment.

The formula for outstanding balance on a standard amortization loan is:

Outstanding Balance at time t = Payment * (1 - v^(n-t))/i where v = 1/(1+i). Plugging and chugging with all this business, we get:
v = 1/(1.0525) = .950119.
Balance at time 5 = 2500 * (1-0.950119^(10-5))/.0525 = 2500 * (1-.774265)/.0525 = 10,749.30

Now, when you answer my initial question, you will go to the initial link I gave you, and this time, press Calculate Payment. Enter new interest rate, time is now 5, and your Present Value is now 10749.30.

Make sense?
the new intrest rate is 7,75

7. Originally Posted by mathceleb
Now, when you answer my initial question, you will go to the initial link I gave you, and this time, press Calculate Payment. Enter new interest rate, time is now 5, and your Present Value is now 10749.30.
I see what you meant, the interest rate goes up 2.5%. I matched your answer within a few cents. Therefore, new interest is 5.25 + 2.5 = 7.75

Staying on this lesson, Annuity Immediate Present Value

we have our Balance at time 5 of 10749.3. Calculate payment, interest is now 7.75, and time left to pay this in 10 years is 5. Press Calculate, we get 2674.52. Subtracting this from our original payment of 2500, we get 174.52.

Things to remember:

When interest rate goes up, payments go up, and Loan Amounts go down.

8. Originally Posted by mathceleb
I'm confused at what you mean by rised 2.5%? is the new interest rate 2.5% or 7.5%?

That being said, we can do 2/3 of the problem before you answer. Here is how you start:

We need the actual loan amount, for that, we need the present Value:

Annuity Immediate Present Value

Calculate Present Value, 5.25 for interest, 2500 for payment, 10 for term and press calculate. PV = 19,072.10 at time 5 after the 5th payment.

The formula for outstanding balance on a standard amortization loan is:

Outstanding Balance at time t = Payment * (1 - v^(n-t))/i where v = 1/(1+i). Plugging and chugging with all this business, we get:
v = 1/(1.0525) = .950119.
Balance at time 5 = 2500 * (1-0.950119^(10-5))/.0525 = 2500 * (1-.774265)/.0525 = 10,749.30

Now, when you answer my initial question, you will go to the initial link I gave you, and this time, press Calculate Payment. Enter new interest rate, time is now 5, and your Present Value is now 10749.30.

Make sense?
i dont understand. cant you calculate it step by step for me i dont even know how to calculate anything of that

9. Originally Posted by Rambo
i dont understand. cant you calculate it step by step for me i dont even know how to calculate anything of that
Did you go to the lesson page, it shows you each step of math line by line. Look above, I matched your answer.

If that doesn't help, let me know, I can walk you through it.

10. Originally Posted by mathceleb
Did you go to the lesson page, it shows you each step of math line by line. Look above, I matched your answer.

If that doesn't help, let me know, I can walk you through it.
i have to learn it for exam cant you calculate it the old fashion way not allowed to use any compt programs in exam!

11. Originally Posted by Rambo
i have to learn it for exam cant you calculate it the old fashion way not allowed to use any compt programs in exam!
Ok, let's go through it step by step. Step 1:

We need to figure out the original value of the loan with annual payments of 2500, @ 5.25% interest, for 10 years. The formula for an annuity paid at the end of a period with level payments is:

Loan = Payment * (1-vⁿ)/i

This formula is extremely important and used for many annuity formulas.

v is a common discount factor in finance. It's simply 1/(1+i). For your problem, it's 1/(1.0525) = 0.9501187648456058.

Therefore, we have Loan = 2500 * (1 - 0.9501187648456058^10)/.0525

0.9501187648456058^10 = 0.5994858752093587

Present Value = 2500 * (1 - 0.5994858752093587)/0.0525
Present Value = 2500 * 0.4005141247906413/0.0525
Present Value = 1001.2853119766032/0.0525
Present Value = 19072.10

I'll stop here, this is step 1. Your original Loan we know is 19072.10. Does this make sense? If so, we will move on to step 2 when you are ready.

12. Originally Posted by mathceleb
Ok, let's go through it step by step. Step 1:

We need to figure out the original value of the loan with annual payments of 2500, @ 5.25% interest, for 10 years. The formula for an annuity paid at the end of a period with level payments is:

Loan = Payment * (1-vⁿ)/i

v is a common discount factor in finance. It's simply 1/(1+i). For your problem, it's 1/(1.0525) = 0.9501187648456058.

Therefore, we have Loan = 2500 * (1 - 0.9501187648456058^10)/.0525

0.9501187648456058^10 = 0.5994858752093587

Present Value = 2500 * (1 - 0.5994858752093587)/0.0525
Present Value = 2500 * 0.4005141247906413/0.0525
Present Value = 1001.2853119766032/0.0525
Present Value = 19072.10

I'll stop here, this is step 1. Your original Loan we know is 19072.10. Does this make sense?

there should be another easier formula to this isnt there?

13. Originally Posted by Rambo
there should be another easier formula to this isnt there?
No. This is the formula for calculating annuities that are used such as home and car loans as well as pensions. It's called an annuity immediate. That means it's payable at the end of the period.

The way i learned fast in class, and at work, is to calculate v first. Then plug that into the annuity formula and figure out the loan amount.

Here is a formal writeup from my site on annuities:

Present Value of Annuity Immediate

Do you want me to go on, or do you want to review what I've put down?

Here is a nice writeup on annuities and perpetuities as well from Wikipedia:

Time value of money - Wikipedia, the free encyclopedia

14. $
A = 5000 \sum _{k=1} ^{8} 1.04^k
$

$
+5000(1.04)^4 +5000(1.04)^3 +5000(1.04)^2 +5000(1.04)^1
$

There should be a formula so you could calculate it something like this???!!

Aint i right???

15. Originally Posted by Rambo
$
A = 5000 \sum _{k=1} ^{8} 1.04^k
$

$
+5000(1.04)^4 +5000(1.04)^3 +5000(1.04)^2 +5000(1.04)^1
$

There should be a formula so you could calculate it something like this???!!

Aint i right???
Yes!!! Good work! The formula I gave you is the sum of the series. But for loans with 10, 20, 30, payments, do you really want to be writing up and adding up all those terms that way?

If so, change your 5000 to 2500, and your 1.04 to (1/1.0525).

For instance your loan payments discounted back to time 0 are:

2500/1.0525 + 2500/(1.0525^2) + 2500/(1.0525^3) + ... + 2500/(1.0525^10)

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