Exam 6: Mathematics of Finance

If $6,000 is deposited at the end of each half year in an account that earns an annual rate of 6.3% compounded semiannually, how long will it be before the account contains $170,000? Round your answer to two decimal places. ​

Find the 63th term of the arithmetic sequence with first term 25 and tenth term 61. ​

Decide whether the problem relates to an ordinary annuity or an annuity due. A retiree inherits $100,000 and invests it at an annual rate of 7.7%, compounded monthly, in an annuity that provides an amount at the end of each month for the next 11 years. Find the monthly amount. ​

A small business owner contributes $5,000 at the end of each quarter to a retirement account that earns an annual rate of 6% compounded quarterly. How long will it be until the account is worth $150,000? ​

A developer wants to buy a certain parcel of land. The developer feels she can afford payments of $26,000 each half-year for the next 6 years. How much can she borrow and hold to this budget at an annual rate of 7.2% compounded semianually? Round your answer to the nearest cent. ​

Find the future value of an annuity due of $1,700 each month for 4 years if the annual interest rate is 11%, compounded monthly. Round your answer to the nearest cent. ​

During four years of college, Nolan MacGregor's student loans are $4,900, $3,800, $3,700, and $4,600 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. 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. After the grace period, the loan is amortized over the next 10 years at an annual rate of 3%, compounded quarterly. Find the quarterly payment. Round your answer 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. ​ ​ ​ ​

Gail Kelley deposits $600 in an account at the beginning of each 3-month period for 8 years. If the account pays interest at the annual rate of 7%, compounded quarterly, how much will she have in her account after 8 years? Round your answer to the nearest cent. ​

What does the number 0.06 represent in the given equation: . ​

Suppose you are offered a job paying a starting salary of $23,000 with yearly raises of $1,300. How much will you receive for your 10th year on the job? ​

To help their son buy a car on his 16th birthday, a boy's parents invest $800 on his 11th birthday. If the investment pays an annual rate of 11% compounded continuously, how much is available on his 16th birthday? Round your answer to the nearest cent. ​

A debt of $8,800 is to be amortized with 8 equal semiannual payments of $1,417.12. If the annual interest rate is 12% compounded semiannually, find the unpaid balance immediately after the 5th payment. Round your answer to the nearest cent. ​

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

A recent college graduate begins a savings plan at age 27 by investing $500 at the end of each month in an account that earns an annual rate of 8.3%, compounded monthly. Suppose this plan is followed for 10 years, and that sufficient equal monthly contributions are made for the next 28 years in order to be able to withdraw $10,000 at the end of each month from the account for the next 25 years. What is the total amount contributed? Round your answer to the nearest cent. ​

How long does it take for $6,000 invested at 9% annual simple interest to be worth $10,500? Round your answer to two decimal places. ​

What is the present value of an investment at 15% annual simple interest if it is worth $924.50 in 6 months? Round your answer to the nearest cent. ​

Christine Parks received a trust fund inheritance of $10,000 on her 30th birthday. She plans to use the money to supplement her income with 24 quarterly payments beginning on her 60th birthday. If the money is worth an annual rate of 8% compounded quarterly, how much will each quarterly payment be? Round your answer to the nearest cent. ​

During four years of college, Nolan MacGregor's student loans are $4400, $4800, $4500, and $4300 for freshman year through senior year, respectively. Each loan amount gathers interest of annual rate of 1%, compounded quarterly while Nolan is in school; and an annual rate of 3%, compounded quarterly during a 6-month grace period after graduation. 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. After the grace period, the loan is amortized over the next 10 years at an annual rate of 3%, compounded quarterly. Suppse Nolan decides to pay an additional $90 above the calculated quarterly payment, how much will Nolan save by paying the extra $90 with each payment? Round your answer to the nearest cent. ​

A young couple buying their first home borrows $72,000 for 28 years at 8.8%, compounded monthly, and makes payments of $577.59. After 2 years, they are able to make a one-time payment of $5,000 along with their 24^th payment. How much will the couple save over the life of the loan by paying the extra $5,000? Round your answer to the nearest dollar. ​