Chapter 8: Problem 13
What is a mortgage?
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
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Chapter 8: Problem 13
What is a mortgage?
These are the key concepts you need to understand to accurately answer the question.
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In Exercises 1-10, \((n)\) a. Find the value of each annuity. Round to the nearest dollar. b. Find the interest. $$ \begin{array}{|l|l|l|} \hline \text { Periodic Deposit } & \text { Rate } & \text { Time } \\ \hline \begin{array}{l} \$ 2000 \text { at the end of } \\ \text { each year } \end{array} & \begin{array}{l} 5 \% \text { compounded } \\ \text { annually } \end{array} & 20 \text { years } \\ \hline \end{array} $$
a. Suppose that between the ages of 22 and 40 , you contribute \(\$ 3000\) per year to a \(401(\mathrm{k})\) and your employer contributes \(\$ 1500\) per year on your behalf. The interest rate is \(8.3 \%\) compounded annually. What is the value of the \(401(\mathrm{k})\), rounded to the nearest dollar, after 18 years? b. Suppose that after 18 years of working for this firm, you move on to a new job. However, you keep your accumulated retirement funds in the \(401(\mathrm{k})\). How much money, to the nearest dollar, will you have in the plan when you reach age \(65 ?\) c. What is the difference between the amount of money you will have accumulated in the \(401(\mathrm{k})\) and the amount you contributed to the plan?
a. Suppose that between the ages of 25 and 37 , you contribute \(\$ 3500\) per year to a \(401(\mathrm{k})\) and your employer matches this contribution dollar for dollar on your behalf. The interest rate is \(8.25 \%\) compounded annually. What is the value of the \(401(\mathrm{k})\), rounded to the nearest dollar, after 12 years? b. Suppose that after 12 years of working for this firm, you move on to a new job. However, you keep your accumulated retirement funds in the \(401(\mathrm{k})\). How much money, to the nearest dollar, will you have in the plan when you reach age 65 ? c. What is the difference between the amount of money you will have accumulated in the \(401(\mathrm{k})\) and the amount you contributed to the plan?
In Exercises 11-14, use the formula $$ A=\frac{P\left[\left(1+\frac{r}{n}\right)^{n t}-1\right]}{\left(\frac{r}{n}\right)} $$ Round all computations to the nearest dollar. Suppose that you drive 40,000 miles per year and gas averages \(\$ 4\) per gallon. a. What will you save in annual fuel expenses by owning a hybrid car averaging 40 miles per gallon rather than an SUV averaging 16 miles per gallon? b. If you deposit your monthly fuel savings at the end of each month into an annuity that pays \(5.2 \%\) compounded monthly, how much will you have saved at the end of six years?
Describe what happens to the portions of payments going to principal and interest over the life of an installment loan.
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