Exam 5: Mathematics of Finance

Robin, who is self-employed, contributes $5,500/year into a Keogh account. How much will he have in the account after 15 years if the account earns interest at the rate of 8.5%/year compounded yearly? ​

Find the present value of an ordinary annuity of $1,400 payments each made semiannually over 8 years and earning interest at 12% per year compounded semi-annually. ​

Moderne Furniture Company had sales of $1,600,000 during its first year of operation. If the sales increased by $110,000/year thereafter, find Moderne's sales in the fifth year. $__________ Find its total sales over the first 5 yr of operation. $ __________

Find the accumulated amount A if the principal P = $10,000 is invested at the interest rate of r = 5% per year for t = 8.5 years, compounded quarterly. ​

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. ​ If a₁, a₂, a₃, ..., an and b₁, b₂, b₃, ..., bn are arithmetic progressions, then a₁ +b₁, a₂ +b₂, a₃ +b₃, ..., an + bn is also an arithmetic progression.

Find the periodic payment R required to amortize a loan of P dollars over t years with interest earned at the rate of r %/year compounded m times a year. Please round the answer to the nearest cent. ​ ​ R = $__________

Andrea, a self-employed individual, wishes to accumulate a retirement fund of $240,000. How much should she deposit each month into her Keogh account, which pays interest at the rate of 7.5%/year compounded monthly, to reach her goal upon retirement 24 years from now? Round your answer to the nearest cent. ​

Find the effective rate corresponding to nominal rate %/year compounded monthly. Round the answers to the nearest hundredth of percent. ​

The management of Gibraltar Brokerage Services anticipates a capital expenditure of $18,000 in 3 years' time for the purpose of purchasing new fax machines and has decided to set up a sinking fund to finance this purchase. If the fund earns interest at the rate of 12 %/year compounded quarterly, determine the size of each (equal) quarterly installment that should be deposited in the fund. Please round the answer to the nearest cent. $__________

Five years ago, Diane secured a bank loan of $310,000 to help finance the purchase of a loft in the San Francisco Bay area. The term of the mortgage was 35 yr, and the interest rate was 12%/year compounded monthly on the unpaid balance. Because the interest rate for a conventional 35-yr home mortgage has now dropped to 10%/year compounded monthly, Diane is thinking of refinancing her property. How much less would Diane's monthly mortgage payment be if she refinances? Please round the answer to the nearest cent.

As a fringe benefit for the past 8 years, Colin's employer has contributed $50 at the end of each month into an employee retirement account for Colin that pays interest at the rate of 8%/year compounded monthly. Colin has also contributed $2,000 at the end of each of the last 4 years into an IRA that pays interest at the rate of 10%/year compounded yearly. How much does Colin have in his retirement fund at this time? ​

Find the interest rate needed for an investment of $4,000 to grow to an amount of $5,000 in 3 yr if interest is compounded continuously. Please round the answer to the nearest hundredth of percent. ​

Find the amount of an ordinary annuity of 5 yearly payments of $600 that earn interest at 5% per year, compounded annually. ​

Find the amount of an ordinary annuity for 6 years of semiannually payments of $1,400 that earn interest at 8%/year compounded semi-annually. ​

Find how much money should be deposited in a bank paying interest at the rate of 10.5%/year compounded quarterly so that at the end of 5 years the accumulated amount will be $60,000. Round your answer to the nearest cent. $ __________

Kunwoo wished to go from airport to his hotel, which is 22 mi away. The taxi rate is $8.00 for the first mile and the $1.50 for each additional mile. The airport limousine also goes to his hotel and charges a flat rate of $17.00. How much money will he save by taking the airport limousine? ​

Find the sum of the first 13 terms of the arithmetic progression: 3, - 4, - 11,... ​

A sum of $100,000 is to be repaid over a 10-year period through equal installments made at the end of each year. If an interest rate of 11%/year is charged on the unpaid balance and interest calculations are made at the end of each year, determine the size of each installment so that the loan (principal plus interest charges) is amortized at the end of 10 years. Round your answer to the nearest cent. R = $__________

Find the 50th term and sum of the first 50 terms of the geometric progression - 2, 2, - 2, 2,... ​

Find the amount of an ordinary annuity for years of weekly payments of $ that earn interest at % per year compounded weekly. ​