Exam 7: Mathematics of Finance

Jenny Reed bought SSX stock for $18 per share. The annual dividend was $3.00 per share, and after 5 year(s), SSX was selling for $44 per share. Find the simple interest rate of growth of her money to the nearest hundredth of a percent. Round your answer to two decimal places.

A house is rented for $3,900 per quarter, with each quarter's rent payable in advance. If money is worth 5%, compounded quarterly, and the rent is deposited in an account, what is the future value of the rent for two years? Round your answer to the nearest cent. ​

What is the fifth term of the sequence whose n^th term is ? ​

Suppose that Scott Andrews deposits his $10,500 bonus in an account that earns an annual rate of 7.0%, compounded quarterly, and makes additional deposits of $700 at the end of each quarter for the next 24.5 years, until he retires. To supplement his retirement, Scott wants to make withdrawals at the end of each quarter for the next 15 years (at which time the account balance will be $0). What is the total amount withdrawn? Assume the interest rate remains the same during Scott's retirement. Round your answer to the nearest cent. ​

Andre De Quadros bought a $3,500, 9-month certificate of deposit (CD) that would earn 9.0% annual simple interest. What is the value of the CD when it matures? Round your answer to to the nearest cent.

The following figure shows a graph that compares the present values of two ordinary annuities of $800 quarterly as functions of the number of quarters. One annuity is at an annual rate of 6% compounded quarterly, and the other is at 9% compounded quarterly. What present value is required to purchase an annuity of $800 a quarter for 25 years with an interest rate of 9% compounded quarterly? Check your answer against the graph. Round your answer to the nearest cent. ​ ​

AdriAnne and Anna's Auto Repair wants to add a new service bay. How much can they borrow at an annual rate of 5%, compounded quarterly, if the desired quarterly payment is $6,100? Assume a loan period of 4.5 years. Round your answer to the nearest cent. ​

A company that purchases a piece of equipment by borrowing $500,000 for 8 years at an annual rate of 6.5%, compounded monthly, has monthly payments of $6,693.12. Find the unpaid balance on this loan after 1 year. Round your answer to the nearest cent. ​

Suppose Becky has her choice of $10,000 at the end of each month for life or a single prize of $1.5 million. She is 35 years old and her life expectancy is 40 more years. If she takes the $1.5 million, spends $700,000 of it, and invests the remainder at an annual rate of 7.0% compounded monthly, what monthly annuity will she receive for the next 40 years? Round your answer to the nearest cent. ​

Suppose that Bob delays starting an IRA for the first 10 years he works but then makes $2,500 deposits at the end of each of the next 15 years. If the annual interest rate is 7.2%, compounded annually, and if he leaves the money in his account for 5 additional years, how much will be in his account at the end of the 30-year period? Round your answer to the nearest cent.

Use a spreadsheet or financial program on a calculator or computer to develop the first two rows of an amortization schedule for a 4-year car loan if $16,300 is borrowed at 8.0%, compounded monthly. ​

Suppose that Ian Greitzer deposits his $13,000 bonus in an account that earns an annual rate of 8.5%, compounded quarterly, and makes additional deposits of $400 at the end of each quarter for the next 21.5 years, until he retires. How much was deposited? Round your answer to the nearest cent. ​

If inflation causes the cost of automobiles to increase by 3.5% each year, what should a car cost today if it cost $21,000 4 years ago? Round your answer to the nearest cent. ​

Write the fourth term of the sequence whose n^th term is ? ​

Rank each interest rate and compounding scheme in order from highest yield to lowest yield. ​

A small business owner contributes $5,000 at the end of each quarter to a retirement account that earns an annual rate of 8.5% compounded quarterly. Suppose when the account reaches $300,000, the business owner increases the contributions to $8,000 at the end of each quarter. What will the total value of the account be after 13 more years since when the account reached? Round your answer to the nearest cent. ​

Time-share sales provide an opportunity for vacationers to own a resort condo for 1 week (or more) each year forever. The owners may use their week at their own condo or trade the week and vacation elsewhere. Timeshare vacation sales usually require payment in full or financing through the time-share company, and interest rates are usually in the 13% to 18% range. Suppose the cost to buy a 1-week time share in a 3-bedroom condo is $21,100. Also suppose a 8% down payment is required, with the balance financed for 18 years at an annual rate of 13.2%, compounded monthly. Find the monthly payment. Round your answer to the nearest cent. ​

Find : . ​

A grateful alumnus wishes to provide a scholarship of $1,800 per year for 4 years to his alma mater, with the first scholarship awarded on his 59th birthday. If the money is worth an annual rate of 5.1%, compounded annually, how much money must he donate on his 49th birthday? Round your answer to the nearest cent. ​

State whether the problem relates to an ordinary annuity or an annuity due. Jane Adele deposits $600 in an account at the beginning of each 3-month period for 10 years. If the account pays interest at the annual rate of 6%, compounded quarterly, how much will she have in her account after 10 years? ​