Annuity Problem.
A house cost $250,000 cash. A purchaser will pay $50,000 cash and a sequence of 8 annual payments, the first due at the end of 3 years. If moiney is worth 7%. Find the annual payment.

Question

caominhim · Answer

$$A = P(1-\frac{r}{100})^{n}$$

caominhim · Answer

and if the buyer pays 50,000 cash you will have 0 interest and a very happy seller

anonymous · Answer

then what's next?

caominhim · Answer

did you mean 250,000 cost? or 5,000 down?

anonymous · Answer

250, 000 cost

anonymous · Answer

how to solve it...

wolf1728 · Answer

Is this really an annuity problem?
Seems more like a loan or a mortgage problem.

anonymous · Answer

i need help to solve this.

anonymous · Answer

i do not know how to solve this, can someone help?

tkhunny · Answer

Basic Principles

i = 0.07
v = 1/(1+i)
d = iv
250000 = 50000 + Pv^3 + Pv^4 + ... + Pv^10

$200000 = P\dfrac{v^{3} - v^{11}}{1-v} = P\dfrac{v^{3}}{d}\left(1-v^{8}\right) = P\dfrac{v^{2}}{i}\left(1-v^{8}\right)$

These never have to be tricky.  Just build them.

anonymous · Answer

what is P?

tkhunny · Answer

"Find the annual payment."

P = The Annual Payment
Normally, I would define that up front.  Must have been typing in my sleep.

You must do the arithmetic.

You must first understand how it came to be.