Exam 6: Mathematics of Finance

A woman buys a car for $45,000. If the interest rate on the loan is 10%, compounded monthly, and if she wants to make monthly payments of $800 for 4 years, how much must she have for a down payment? Round your answer to the nearest dollar. ​

A young executive deposits $200 at the end of each month for 5 years and then increases the deposits. If the account earns an annual rate of 8.1%, compounded monthly, how much (to the nearest dollar) should each new deposit be in order to have a total of $300,000 after 17 years from the time the deposits were increased? Round your answer to the nearest cent. ​

A company that purchases a piece of equipment by borrowing $300,000 for 9 years at an annual rate of 6%, compounded monthly, has monthly payments of $3,601.72. Find the unpaid balance on this loan after 1 year. Round your answer to the nearest cent. ​

During four years of college, Nolan MacGregor's student loans are $4,600, $3,500, $3,800, and $5,000 for freshman year through senior year, respectively. Each loan amount gathers interest of annual rate 1%, compounded quarterly while Nolan is in school; and an annual rate of 3%, compounded quarterly during a 6-month grace period after graduation. What is the loan balance after the grace period? Assume the freshman year loan earns an annual rate of 1% interest for 3/4 year during the first year, then for 3 full years until graduation. Make similar assumptions for the loans for the other years. Round your answer to the nearest cent. ​

Suppose a new business makes a $1,000 profit in its first month and has its profit increase by 9% each month for the next 2 years. How much profit will it earn in its first year? Round your answer to the nearest cent. ​

Find the future value of an ordinary annuity of $67 paid quarterly for 4 years, if the interest rate is 6%, compounded quarterly. Round your answer to the nearest cent. ​

If $3,000 is deposited at the beginning of each quarter into an account that earns 6% compounded quarterly, how long until the account contains $42,000? Express your answer as a whole number of quadrants. ​

A recent college graduate buys a new car by borrowing $20,000 at 8.4%, compounded monthly, for 5 years. She decides to pay an extra $14 per payment. How many payments (that include the extra $14) will she make, including the final partial payment? ​

Jenny Reed bought SSX stock for $15 per share. The annual dividend was $1.50 per share, and after 2 year(s), SSX was selling for $38 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. ​

Find the future value if $4200 is invested for 2 years at an annual rate of 11% compounded quarterly. Round your answer to the nearest cent. ​

A woman buys an apartment house for $1,250,000 by making a down payment of $375,000 and amortizing the rest of the debt with semiannual payments over the next 12 years. The annual interest rate on the debt is 7.5%, compounded semiannually. Find the total amount paid over the life of the loan (excluding the down payment). Round your answer to the nearest cent. ​

A young couple wants to have a college fund that will pay $25,000 at the end of each half-year for 8 years. If they can invest at annual rate of 8%, compounded semiannually, how much do they need to invest at the end of each 6-month period for the next 18 years in order to begin making their college withdrawals 6 months after their last investment? Round your answer to the nearest cent. ​

Find the next three terms of the geometric sequence. ​ 25, 5, 1,... ​

Find the interest that will result if $10,500 is invested at an annual rate of 9%, compounded continuously, for 12 years. 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. ​

Recent sales of some real estate and record profits make it possible for a manufacturer to set aside $880,000 in a fund to be used for modernization and remodeling. How much can be withdrawn from this fund at the beginning of each half year for the next 4 years if the fund earns an annual rate of 7.6%, compounded semiannually? Round your answer to the nearest cent. ​

A woman buys an apartment house for $1,250,000 by making a down payment of $125,000 and amortizing the rest of the debt with semiannual payments over the next 10 years. The annual interest rate on the debt is 7.5%, compounded semiannually. Find the total interest paid over the life of the loan. Round your answer to the nearest cent. ​

Given 10 and 30 year loans with the same interest rate, the 30 year loan results in a lower periodic payment.

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 7.3% compounded monthly, what monthly annuity will she receive for the next 40 years? 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? ​