Final answer:
To determine the effective interest rate, one must consider the compounding frequency, which is not specified in the question. Loan repayments and potential savings from additional payments can be calculated using the provided formula. Bond valuation changes with market interest rates, and the value decreases if the bond's rate is below the market rate.
Step-by-step explanation:
Calculating the Effective Interest Rate and Bond Valuation
To find the effective interest rate per payment period, we need to adjust the nominal annual interest rate for the frequency of compounding. However, additional information is required, such as the compounding period (monthly, quarterly, etc.), to provide a specific answer.
Regarding the $300,000 loan with a 6% interest rate, convertible monthly over 30 years, the monthly payments can be calculated using the formula provided. By making a larger payment equivalent to a fraction of 12, you effectively make 13 payments a year, which can substantially reduce both the total interest paid over the life of the loan and the loan's amortization period.
For the question on the water company's bond, with a change from a 6% to a 9% interest rate one year before maturity, we'd expect the market price of the bond to decrease, as it now offers an interest rate below the new market rate. The specific price you'd be willing to pay can be calculated by discounting the expected final payments by the current market interest rate.
In the case of a bond with an interest rate lower than the current market rate of 12%, the bond price would be such that the expected return over the next year equates to the current market rate. Given the computation shown, $964 would be the maximum you would pay for a $1,000 bond expecting to receive $1,080 in a year's time.