Final answer:
To determine the principal repaid in the first six payments of a loan, we would use the present value of an annuity formula. For a loan with 6% interest convertible monthly, we calculate the monthly interest rate and solve the formula for monthly payment. We can also assess the benefits of making additional payments yearly.
Step-by-step explanation:
The subject of this question is the amortization of a loan with an understanding of how to calculate the amount of principal repaid in the first six payments, given the present value of an annuity factor.
The question provided was somewhat misguided since it did not relate directly to the example of the $300,000 loan with 6% interest convertible monthly over 30 years. However, using similar principles, we would determine the monthly payment by using the present value formula for an annuity.
For example, to calculate the monthly payment of a $1,000,000 house loan over 30 years at a nominal interest rate of 6% convertible monthly, we would assume:
Once we have the monthly payment, we can also examine the impact of making an additional payment per year, effectively 13 instead of 12, and how it would reduce the length and total cost of the loan. The key is understanding how to manipulate the formula and the variables to find the desired outcomes.
If we have a simple interest loan, we can use formulas such as Interest = Principal × rate × time to calculate the total interest paid over a period or to determine the interest rate if we know the amount of interest accrued on a principal over a certain time.