Question

3. (5 points) An investment vehicle promises to pay you $1,000 in year 1, $2,000 in year 2, $3,000 in year 3 and $4,000 in year 4, provided you deposit $X with them today. If this is a fair deal and the interest rate is 9%, how much is X?

Answer 1

Given,

Cash flow for year 1 ( CF₁ ) = $ 1000 , n₁ = 1

Cash flow for year 2 ( CF₂ ) = $ 2000 , n₂ = 2

Cash flow for year 3 ( CF₃ ) = $ 3000 , n₃ = 3

Cash flow for year 4 ( CF₄ ) = $ 4000 , n₄ = 4

Interest rate (r) = 9% or 0.09

Solution :-

the present value Here, 'X' is of given payments. X = $1000 (1+0.09) & $2000 $2000 & $3000 (1+0.092 T (1+0.09) 3 a $4000 (1+0.094 x = $1000 1.09 $2,000 11.092 $3000 (1.09) 3 $4000 11.0904 - $1000 $2000 $3000 $4000 - ting ti 1881 + 1295029 TIYU58161 X= $917.4311.9266+ $1683.35998653+$7316.55044 + $7833.70084426 x = $7751