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December 12th, 2010, 03:16 AM   #1
Joined: Dec 2010

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Annuity and serial loan, capable to pay for it after n years

Hi there!
I'm preparing myself for my examination and have a case I'm pretty sure will be given at it - but we don't have a specific formula for this case, and we are five guys trying to find a simpler way to solve this.

Let's assume that you take a loan, 50.000 USD, which you are to pay yearly during the next 20 years with an interest of 5%. In short:

K0 = 50.000 USD (fifty-thousand)
n = 20
r = 0,05 (p.a.)

To figure out what you pay can be done by:

How much you pay every period by annuity loan:
K = ( K0 * r ) / ( 1 - ( 1 + r )^n

Total paid in interest:
n * K - K0

How much you pay every period by serial loan:
(K0 * r ( n + 1 )) / 2

The case:
Assume that you, i.e.:
inherited a lot of money, or
sold your property and got a higher return than what it cost you, or
won in lottery,

and by that, five years into this you paid for your entire loan. How much did you pay in
1) total?
2) instalments?
3) interest?

I can calculate this by calculating how much one pays every period, calculate rent for the given period, calculate instalment for the given period, by that figure out how much of the loan is left to pay for the next period, and so it continues. But doing this over and over again takes a lot of time and I was wondering if there is any formula for figuring out this an easier way.

And if anyone know of a solution for annuity as well as serial loan, we would be very happy for it!

If you think my english isn't all correct then you're probably right, greetings from Norway!

ShellShock is offline  

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