Question

Hi guys i got a question regarding present value of annuity. First of all, i understand the general idea of present value of annuity, for example if i were to receive a series of $1000 repeatedly for the next 10 years, to find the present value of the annuity, i would need to take each and every one of these future cash flows and divide it by (1+i)^n where "i" is risk-free interest rate of the market and "n" is the year in which the money was received. In doing so i am able to find the value equivalent of the money i would receive and benchmark it with todays value.

Answer 1

(sorry post was too long) Now things gets confusing for me when i start to deal with mortgage payments or payments in general.

lets say i buy a house at $800000 and the 30-year-fixed rate of mortgage is 5.7% and i am suppose to find the monthly payment. How do i use FV=PV x (1+ i)^n to solve this question? i do know how to input the values and get the correct answer but i do not know what does future value of the house mean, nor do i understand why the interest rate in this case is using 5.7% (i.e 5.7%/12). Are they saying that the house would be valued at 800000x(1 + 0.00475)^360 in the future?

Answer 2

someone please help me :( i gotta sleep already, ill be back tomorrow. see ya

Answer 3

If you have a financial calculator, the inputs are:
N = 360
r = 0.475%
PV = 800000
FV = 0 (because after 360 months, you'll pay off all the debt)
Compute payments you get 4643.2

If you want to do the math... THENNNN
Use this formula http://www.financeformulas.net/Annuity_Payment_Formula.html (scroll down for explanation of the formula)
r = 0.00475
PV = 800000
n = 360
You should get 4643.2.

Answer 4

FV=PV x (1+ i)^n is not a formula for annuity btw.

Answer 5

the formula for present value of annuity is PV=FV/(1+i)^n , but if you say that FV is 0for this mortgage payment, then does that mean that PV would also be 0?

Answer 6

No, that formula is for 1 single cash flow. Annuities, as you said, are multiple cash flows.

Answer 7

but the derivation for PV of annuity comes from the future value of annuity/ (1+i)^n
where FV annuity= a(1- r^n)/(1-r)