Final answer:
The credit to cash from discounting a note is calculated by subtracting the discount amount, found by applying the discount rate to the note's value, from the note's value itself. In this case, a $20,000 note discounted at an 8% rate provides a credit to cash of $18,400. A similar approach is used for calculating the present value of bond payments at different discount rates.
Step-by-step explanation:
To calculate the credit to cash from discounting a note, you need to apply the discount rate to the note's value. With a $20,000 note and an 8% discount rate, you multiply $20,000 by 8% to find the discount amount, which is $1,600. Then you subtract this discount from the note's value to find how much cash will be credited, which would be $20,000 - $1,600 = $18,400.
For example, applying this to a 2-year bond with an 8% annual interest and a principal value of $3,000, you would receive $240 in interest each year. To find the present value (PV) at the same 8% discount rate, you discount the interest payments and the principal repayment. The calculation using the present value formula would be:
- PV of first year's interest: PV = $240 / (1 + 0.08)^1 = $222.22
- PV of second year's interest and principal: PV = ($240 + $3,000) / (1 + 0.08)^2 = $2,777.78
The total present value is the sum of these: $222.22 (first year) + $2,777.78 (second year) = $3,000.00. If the discount rate increases to 11%, the present value would decrease because future cash flows are discounted more heavily.