Suppose that you take out a $250,000 house mortgage from your local savings bank. Thebank requires you to repay the mortgage in equal annual installments over the next 30 years.It must therefore set the annual payments so that they have a present value of $250,000.
Question
Suppose that you take out a 250,000.
Solution 1
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Solution 2
You haven't provided a specific question to answer. However, if you're asking how to calculate the annual payment for the mortgage, here's how you can do it:
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First, you need to know the interest rate. Let's assume it's 5% per year.
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Convert the annual interest rate into a decimal by dividing by 100. So, 5% becomes 0.05.
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The formula to calculate the annual payment is: P = [r*PV] / [1 - (1 + r)^-n], where P is the payment, r is the interest rate (in decimal), PV is the present value of the loan (i.e., the amount of the loan), and n is the number of payments (in this case, 30 years).
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Plug the values into the formula: P = [0.05 * 250,000] / [1 - (1 + 0.05)^-30].
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Solve the equation to find the annual payment.
Remember, this is a simplified example and actual mortgage calculations may include other factors like property taxes, insurance, etc. Also, interest rates on mortgages are usually compounded monthly, not annually. This example is just to give you a basic understanding of how the calculation works.
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