Its A geometric progression question

Question

Find the present value of anually that yields an income of $12000 at end of each year for 10 years, assuming that the interest rate is 7% compounded anually.

Answer 1

The related formula:

P = p((1 - (1 / ( 1+r)^-n))/ r)

P represents the presents value

p represents the annual payment

r represents the rate

n represents the number of payments to be received

For your data

P = 12000((1 / (1.07)^-10)) / 0.07

Can you calculate and answer?

Answer 2

I will not do the computation for you, but I will tell you how to do it.

a₁₀ = (1 - v¹⁰)/i where i=.07 and v = 1/(1.07)

Your answer is 12000a₁₀.

The formula comes from v + v² + v³ +...+ v¹⁰ = v(1-v¹⁰)/(1-v);

this is the present value of an annuity of $1 per year for 10 years.

P.S.

Your question should read "annuity", not anually!