Answer:
$74.14
Explanation:
first we must calculate the market price of the bond:
0.03 = {40 + [(1,000 - MV)/20]} / [(1,000 + MV)/2]
0.03 x [(1,000 + MV)/2] = 40 + [(1,000 - MV)/20]
0.03 x (500 + 0.5MV) = 40 + 50 - 0.05MV
15 + 0.015MV = 90 - 0.05MV
0.065MV = 75
MV = 75 / 0.065 = $1,153.85
so the customer borrowed $1,153.85
in 10 years, the principal + interest will = $1,153.85 x (1 + 5%)¹⁰ = $1,879.50
the customer will receive:
20 semiannual payments of $40, the future value = $40 x 22.841 (FV annuity factor, 2%, 19 periods) + $40 = $953.64
bond's face value = $1,000
total money received = $1,000 + $953.64 = $1,953.64
net gains = $1,953.64 - $1,879.50 = $74.14
