# Investing in strip bonds (part 2): Discount pricing and compound interest is the name of the game In our article Investing in strip bonds (part 1), we introduced you to the features and benefits of strips.

To recap: Standard, conventional bonds have two parts: the face value, or principal, and the coupons. Upon maturity, the investor receives the face value and in the meanwhile, also receives regular coupon payments, which are a fixed percentage of the face value of the bond. The strip bond is a fixed income investment created when a standard bond is deconstructed.

To create a strip bond, the coupons of a standard bond are separated — stripped — from the principal. The remaining bond principal (called a "residual") and each coupon are sold at a discount and mature at face value.

Here's where it gets interesting: even though strips don't provide interest payments, prices for long-term strips (more than a year) are determined with a calculation that assumes compound interest, as distinguished from simple interest.

In this article we'll break down that calculation. Even if financial formulas aren't your thing, it's interesting to see how compounding is built in to strip bond investing, even though strips don't provide regular coupon payments.

First let's consider short-term money market instruments. These are instruments, such as T-bills, that have a duration of less than a year. To determine the discount price of those, the financial community uses a variation of a simple interest calculation. (Oddly enough, by convention, this calculation uses a 360-day year.) The calculation is:

Face value — (annualized bank discount yield x face value x days held to maturity / 360)

With long-term strips that extend over many years, even though you do not receive coupon interest payments, the formula used to calculate the discounted price of the strip assumes compound interest. The formula accounts for the principal invested being compounded at the prevailing market interest rate at the time of purchase, during the life of the strip, up to the maturity date, using the time value of money calculation for present value:

PV = FV / (1 + i)n

This formula locks in the yield for the duration of the term, annually compounding your return on principal plus previously accrued notional interest for the next year.

Here is an example. You purchase a \$10,000 strip that matures in 15 years and the annual interest rate offered is 5%. Using the present value formula, the purchase price would be approximately \$4,810.17.

PV = \$10,000 / (1 + .05)15

You will earn \$5,189.83 in interest (\$10,000 – \$4,810.17) over the next 15 years.

Now, if you were to take the purchase price of \$4,810.17 and multiply it using a simple interest formula, the earnings in 15 years add up to only \$3,607.63:

\$4,810.17 x 5% x 15 years = 3,607.63

This amount is well short of the \$5,189.83 you will actually receive.

But if you plug in a compounding interest rate formula using 5%, you will get the correct interest amount for the 15 years:

\$4,810.17 x ((1 + 0.05)15 - 1) = 5189.83

Now you know that compounding is built in to strip bond investing, even though strips don't provide regular coupon payments.

## Tax considerations

Be aware that strips that are held to maturity are treated as interest income per Canadian tax laws and not as a capital gain. Even though the income isn't paid until maturity or sale — under tax law an investor must account for the annual accrual of notional interest as investment income in the year earned, not the year received. A capital gain or loss, however, can be triggered if the note is sold prior to the maturity date.

Also, strips are best suited for tax-deferred and tax-sheltered plans such as RRSPs, RRIFs, TFSAs and RESPs. The interest earned inside these plans is not taxable until withdrawn from the plan (or, with a TFSA, not taxable at all) and is tax sheltered while growing and earning inside the plan.