At the beginning of her current tax year, Angela purchased a zero-coupon corporate bond at original issue for $30,000 with a yield to maturity of 6 percent. Given that she will not actually receive any interest payments until the bond matures in 10 years, how much interest income will she report this year assuming semiannual compounding of interest?

The interest that would be reported this year is $1827

Explanation:

The interest on loan for the first six months is calculated thus:

$30000*6%*6months/12months=$900

Thereafter, the next six month interest would be based on the initial investment and the interest earned in the first six months since the interest is compounded interest. In other words, interest is paid on initial investment and also on the interest earned by the initial investment

($30000+$900) * 6%*6months/12months=$927

The total interest earned the investment in the first year is $900+$927=$1827

She will report an interest income of $1,827 for this year.

Explanation:

The yield to maturity is 6%. However, the interest on the bond is compounded semi-annually. Therefore, we need to calculate the interest income for either semi-annual period and then sum the two incomes.

Interest income for first semi-annual period

= $30,000 x 0.06 x 6/12

= $900

Interest income for second semi-annual period

= ($30,000 + $900) x 0.06 x 6/12

= $30,900 x 0.06 x 6/12

= $927

Interest income for the year

= $900 + $927

= $ 1,827