Question

On October 31, Sarah Willis borrowed $5,600 from the Vestal Central Bank. She gave the bank her 90-

day note for that amount. The note was dated October 31, and the exact interest rate was 12%. a. Find
the date of maturity for the note. b. How much did Sarah pay to the bank on the maturity date?

Answer 1

A $3,000 two-year bond with an 8% interest rate will be worth exactly $3,000 in present value terms when discounted at the same interest rate. However, if interest rates rise to 11%, the bond's present discounted value decreases to $2,851.38, reflecting the reduced attractiveness of the bond compared to the higher prevailing rates.

Step-by-step explanation:

Consider a simple two-year bond issued for $3,000 with an interest rate of 8%.

The bond pays $240 in interest each year (which is $3,000 × 8%). At the end of the second year, the bond pays an additional $3,000 in principal.

To determine what this bond is worth in the present, we need to calculate its present discounted value (PDV).

If the discount rate is 8%, the PDV calculation for the first year's interest would be $240 / (1 + 0.08)^1 = $222.22 approximately, and for the second year's interest plus the principal, it would be

($240 + $3,000) / (1 + 0.08)^2 = $2,777.78 approximately.

When combined, the total PDV of the bond at an 8% discount rate is $3,000.

If interest rates rise to 11%, we need to recalculate the PDV.

The first year's interest PDV would be $240 / (1 + 0.11)^1 = $216.22 approximately, and the second year's interest plus principal would be

($240 + $3,000) / (1 + 0.11)^2 = $2,635.16 approximately.

Adding these together results in a lower PDV of $2,851.38 for the bond when the discount rate is 11%, reflecting a decrease in value due to the higher interest rates.