Exam 7: Mathematics of Finance

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. ​

Emily Rideout deposits $2,000 at the end of each of the 5 years she qualifies for an IRA. If she leaves the money that has accumulated in the IRA account for 25 additional years, how much is in her account at the end of the 30-year period? Assume an annual interest rate of 8.1%, compounded annually. Round your answer to the nearest cent. ​

If you borrow $1,700 for 4 years at 5% annual simple interest, how much must you repay at the end of the 3 years? Round your answer to the nearest dollar. ​

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 8.1%, 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 What is the total amount withdrawn? Round your answer to the nearest dollar. ​

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 How much can be withdrawn from this fund at the beginning of each half year for the next 4 years if the fund earns an annual rate of 7.6%, compounded semiannually?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 trust will provide $12,000 to a county library at the beginning of each 3-month period for the next 2.5 years. If the money is worth an annual rate of 6.8%, compounded quarterly, find the amount in the trust when it begins. Round your answer to the nearest cent.

Parents agree to invest $500 (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.

Christine Parks received a trust fund inheritance of $15,000 on her 20th birthday. She plans to use the money to supplement her income with 28 quarterly payments beginning on her 50th birthday. If the money is worth an annual rate of 7.2% compounded quarterly, how much will each quarterly payment be? Round your answer to the nearest cent. ​

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

Suppose that Tom Martin deposits his $11,500 bonus in an account that earns an annual rate of 7%, compounded quarterly, and makes additional deposits of $600 at the end of each quarter for the next 25.5 years, until he retires. To supplement his retirement, Tom wants to make withdrawals at the end of each quarter for the next 13 years (at which time the account balance will be $0). What is the amount of each withdrawal? Round your answer to the nearest cent. ​

A family wants to have a $180,000 college fund for their children at the end of 16 years. What contribution must be made at the end of each quarter if their investment pays an annual rate of 7.4%, compounded quarterly? Round your answer to the nearest cent. ​

What interest will be earned if $5,800 is invested for 2 years at an annual rate of 9% compounded monthly? Round your answer to the nearest cent. ​

How long does it take for $8,000 invested at 11% annual simple interest to be worth $13,000? Round your answer to two decimal places.

Suppose an employee has a base salary of $25,000 per year and at the end of each year a raise of $1,500 will be given. Find the employee's total income after the first 4 years. ​

A professional athlete invested $3.1 million of a bonus in an account that earns an annual rate of 6.8%, compounded semiannually. If $120,400 is to be withdrawn at the end of each six months, how long will it be until the account balance is $0? Round your answer to two decimal places. ​

Which table shows a correct amortization schedule for the loan described? ​ $49,000 for years at an annual rate of 10% compounded semiannually

If a population of 9 million begins to increase at a rate of 0.33% each month, in how many months will it be 14 million? Round your answer to two decimal places. ​

Find the next three terms of the geometric sequence. ​ 4, 16, 64,... ​

What is the 9th term of the geometric sequence with first term 5 and common ratio 2? ​

An investor owns several apartment buildings. The taxes on these buildings total $2,000 per year and are due before April 1. The late fee is 0.5% per month up to 6 months, at which time the buildings are seized by the authorities and sold for back taxes. If the investor has $2,000 available on March 31, how much money will he save by investing the money at 9% and paying the taxes and the penalty on September 30 instead of paying the taxes at that time? Round your answer to the nearest cent. ​