13. [ 9 points] You have \( \$ 3500 \) to invest. You can choose from two accounts in which to invest your money. The first is a simple interest account that earns \( \$ 100 \) each year. The second is a compound interest account that earns \( 3.5 \% \) interest per year. Answer the following questions: a. How long will it take to double your money in the simple interest account? 35 years \( 2 \times 3500=7000 \) \( l=7000-3500=3500 \) \( 100 x t=3500 \) \( t \frac{2500}{100}=35 \).

The principal \( P \) is borrowed at a simple interest rate \( r \) for a period of time \( t \). Find the simple interest owed for the use of the money. Assume 365 days in a year. \( P=\$ 7000, r=4.5 \%, t=18 \) months The simple interest owed for the use of the money is \( \$ \square \). (Do not round until the final answer. Then round to the nearest cent as needed.)

Determine the present value \( P \) that must be invested to have the future value \( A \) at simple interest rate \( r \) after time \( t \). \[ A=\$ 5000, r=2.5 \%, t=6 \text { years } \] The present value \( P \) that must be invested is \( \$ \) (Round up to the nearest cent.)

Advice from most financial advisers states to spend no more than \( 28 \% \) of one's gross monthly income for one's mortgage payment, and to spend no more than \( 36 \% \) of one's gross monthly income for one's total monthly debt. Suppose a family has a gross annual income of \( \$ 43,200 \). a. What is the maximum amount the family should spend each month on a mortgage payment? b. What is the maximum amount the family should spend each month for total credit obligations? c. If the family's monthly mortgage payment is \( 80 \% \) of the maximum they can afford, what is the maximum amount they should spend each month for all other debt? a. The maximum monthly mortgage payment should be \( \$ \square \). b. The maximum monthly total credit obligations should be \( \$ \square \). The maximum amount they should spend monthly on all other debt is \( \$ \)

For the investment situation below, identify the annual interest rate, the length of the investment in years, the periodic interest rate, and the number of periods of the investment. \( 9 \% \) compounded monthly for 3 years (a) the annual interest rate (b) the length of the investment in years (c) the periodic interest rate (d) the number of periods of the investment

Suppose that you camed a bachelor's degree and now youre teaching high school. The school district offers teachers the opportunity to take a year off to eam a master's degree. To achieve this goal, you deposit \( \$ 1000 \) at the end of each year in an annuity that pays \( 5.5 \% \) compounded annually. a. How much will you have saved at the end of five years? b. Find the interest.