Question

Your friend sweetens the deal, and offers you $2,000 in 5 years with 3.5% interest payments every year. What is the fair price to pay today for this promise if you expect to earn 4.5% from the deal?

Group of answer choices $1,912 $1,822 $1,605 $1,977

Answer 1

Given,

Future value = $2000

No. of years (n) = 5 years

Interest rate = 3.5%

Rate of return (r) = 4.5% or 0.045

Solution :-

Interest payment (A) = $2000 x 3.5% = $70

Fair price today = A/r x [1 - (1 + r)^-n] + [future value (1 + r)ⁿ]

= $70/0.045 x [1 - (1 + 0.045)^-5] + [$2000 (1 + 0.045)⁵]

= $70/0.045 x [1 - (1.045)^-5] + [$2000 (1.045)⁵]

= $70/0.045 x [1 - 0.8024510465] + [$2000 1.2461819376]

= $70/0.045 x 0.1975489535 + [$1604.90209]

= $307.29837 + $1604.90209 = $1912

Thus, the fair price to pay today for this promise is $1912.