A 2n-year annuity has deposits of X made at the end of each of the first...

A 2n-year annuity has deposits of X made at the end of each of the first n years and deposits of 2X made at the end of each of the next n years. The accumulated value of this annuity at the end of 2n years is 6000. Suppose that the annual effective rate of interest is i, where i > 0. You are given X i = 1500. Find the present value of this annuity at time t = 0.

Expert Solution

X/i*((1+i)^n-1)*(1+i)^n+2X/i*((1+i)^n-1)=6000

Xi=1500

=>X=1500/i

(1500/i)/i*((1+i)^n-1)*(1+i)^n+2*(1500/i)/i*((1+i)^n-1)=6000

Let (1+i)^n be a

1500/i^2*(a-1)*a+3000/i^2*(a-1)=6000

=>i=100%
=>a=2
=>n=1

Present value of annuity=1500/2+3000/4=1500.00

jeff jeffy answered 2 years ago

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