Interest rate swap payments
1. The idea
In an interest-rate swap, two sides exchange interest payments on the same amount, the notional, which itself never changes hands, as in an FRA. One side pays a fixed rate; the other pays a floating rate, set at the start of each period. Swap rates are quoted as simple yearly rates, so each payment is the rate times the notional times the length of the period in years. On each payment date only the difference changes hands:
\[ \text{net received by the side paying fixed} = (R_{\text{float}} - R_{\text{fix}})\, L\, \Delta t, \]
where \(R_{\text{float}}\) and \(R_{\text{fix}}\) are the floating and fixed rates as decimals, \(L\) the notional and \(\Delta t\) the length of the period in years, 0.5 for payments every six months. The side receiving fixed gets the opposite.
2. Try it
If an answer is wrong, we will see what went wrong and how to fix it.
3. The payments on a chart
In the question, the fixed payment for six months is \(0.04 \times \$10{,}000{,}000 \times 0.5 = \$200{,}000\), and the floating payment \(0.046 \times \$10{,}000{,}000 \times 0.5 = \$230{,}000\). Only the difference changes hands, so we receive $30,000.
Now move the floating rate. What one side receives, the other pays.
4. One worked example, then your turn
The worked example is the side that receives fixed.
Now one with hints, one step at a time.
And one on your own.
5. Practice
Each question has new numbers, paying fixed or receiving fixed. You master the skill when you get three right in a row, with at least one right answer where we receive the net amount and one where we pay it. You can always open the solution, but then that question does not count.
6. Coming back to it
When you have mastered a skill, it comes back on the start page for a short review after 1 day. After each right answer the next review comes later: after 3, 7, 14 and then 30 days. After a wrong one, the reviews start again at 1 day.
This skill: