Exam 6: Mathematics of Finance

Suppose an annuity will pay $12,000 at the beginning of each year for the next 10 years. How much money is needed to start this annuity if it earns 6.7%, compounded annually? Round your answer to the nearest cent. ​

State whether the problem relates to an ordinary annuity or an annuity due. A property owner has several rental units and wants to build more. How much of each month's rental income should be deposited at the beginning of each month in an account that earns an annual rate of 6.9%, compounded monthly, if the goal is to have $200,000 at the end of 7 years? ​

A woman buys an apartment house for $1,250,000 by making a down payment of $325,000 and amortizing the rest of the debt with semiannual payments over the next 11 years. The annual interest rate on the debt is 8%, compounded semiannually. Find the size of each payment. 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 5-year car loan if $16,600 is borrowed at 8%, compounded monthly. ​

Suppose a new business makes a $2,000 profit in its first month and has its profit increase by 14% each month for the next 2 years. How much profit will the business earn in its 13^th month? Round your answer to the nearest cent. ​

A debt of $100,000 is amortized at 6%, compounded monthly, over 25 years with 300 monthly payments of $644.30 each. The figure below includes two graphs: one shows the total amount paid (in monthly payments) as a function of time (in months), and the other shows the amount paid toward the principal of the debt as a function of time. ​ ​ Which of the answers represents how much interest will be paid on the debt after 100 months? ​

If a population of 6 million begins to increase at a rate of 0.2% each month, in how many months will it be 9 million? Round your answer to two decimal places. ​

What lump sum should be deposited in an account that will earn at an annual rate of 7%, compounded quarterly, to grow to $90,000 for retirement in 20 years? Round your answer to the nearest cent. ​

A new firm loses $1,600 in its first month, but its profit increases by $400 in each succeeding month for the rest of its first year. What is its profit in the twelfth month? ​

Write an expression that gives the requested term or sum. ​ The sum of the first 12 terms of the geometric sequence with first term 6 and common ratio 7. ​

Parents agree to invest $800 (at an annual rate of 8%, compounded semiannually) for their son on the December 31 or June 30 following each semester that he makes the Dean's List during his 4 years in college. If he makes the Dean's List in each of the 8 semesters, how much money will his parents have to give him when he graduates? Round your answer to the nearest cent. ​

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

Leah Hagel bought a $4,000, 9-month certificate of deposit (CD) that would earn 7% annual simple interest. Three months before the CD was due to mature, Leah needed her CD money, so a friend agreed to lend her money and receive the value of the CD when it matured. If their agreement allowed the friend to earn a 11% annual simple interest return on her loan to Leah, how much did Leah receive from her friend? Round your answer to the nearest cent. ​

What is the size of the payments that must be deposited at the beginning of each 6-month period in an account that pays an annual rate of 8%, compounded semiannually, so that the account will have a future value of $110,000 at the end of 11 years? Round your answer to the nearest cent. ​

Suppose a young couple deposits $1,100 at the end of each quarter in an account that earns an annual rate of 8.8%, compounded quarterly, for a period of 6 years. After the 6 years, they start a family and find they can contribute only $300 per quarter. If they leave the money from the first 6 years in the account and continue to contribute $300 at the end of each quarter for the next years, how much will they have in the account (to help with their child's college expenses)? Round your answer to the nearest cent. ​

Suppose that Scott Andrews deposits his $14,500 bonus in an account that earns an annual rate of 7.5%, compounded quarterly, and makes additional deposits of $400 at the end of each quarter for the next 21.5 years, until he retires. To supplement his retirement, Scott wants to make withdrawals at the end of each quarter for the next 14 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. ​

What is the 7th term of the geometric sequence with first term 5 and common ratio 2? ​

How much more interest will be earned if $7,500 is invested for 7 years at an annual rate of 12% compounded continuously, instead of at 12% compounded quarterly? 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. ​

A student has a savings account earning 8% simple interest. She must pay $1,400 for first-semester tuition by September 1 and $1,400 for second-semester tuition by January 1. How much must she earn in the summer (by September 1) in order to pay the first-semester bill on time and still have the remainder of her summer earnings grow to $1,400 between September 1 and January 1? Round your answer to two decimal places. ​