Question

An investor purchases a zero coupon bond with 22 years to maturity at a price of $322.58. The bond has a par value of $1,000. What is the implicit interest for the first year? Assume semiannual compounding.

$17.02

$14.90

$17.45

$16.21

$16.46

Answer 1

Answer is $17.02:

Present Value = $322.58
Future Value = $1,000
Time = 22 years or 44 semi-annual periods
Semi-Annual Rate (r ) = ??

Future Value = Present Value * (1 + r)^ n
$1,000 = $322.58 * (1 + r) ^ 44
3.1000 = (1 + r) ^ 44
3.1000 ^ (1/44) = 1 + r
1.02605 = 1 + r
r = 0.02605 or 2.605%

Semi-annual Interest = 2.605%

First Semiannual Period:

Interest = 2.605% * $322.58
Interest = $8.40

Carrying Value = $322.58 + $8.40
Carrying Value = $330.98

Second Semiannual Period:

Interest = 2.605% * $330.98
Interest = $8.62

Implicit Interest for the first year is $17.02 ($8.40 + $8.62)