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???
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 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.
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.
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
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)