Exam 6: Mathematics of Finance

You have two investment opportunities.You can invest $6000 at 12% compounded monthly or you can invest $6100 at 12.1% compounded quarterly.Which has the better effective rate of interest? Use a graphing calculator to graph both amounts as a function of time in years.Which is the better investment over twenty years?

If $25,000 is used to purchase an annuity consisting of equal payments at the end of each year for the next 8 years and the interest rate is 5% compounded annually,find the amount of each payment.

Suppose a person deposits $1000 in a savings account at the end of every six months.What is the value of the account at the end of five years if interest is at a rate of 10% compounded semiannually?

Suppose Lena deposits $500 at the end of every month into a bank account that pays 5.4% compounded monthly.After five years,how much will she have?

A person has the option of satisfying a debt by either paying $5000 now and $5000 in two years,or by paying $3000 now,$3000 a year from now,and a final payment of x dollars two years from now.Determine an equation of value that corresponds to the value of all payments at the end of two years.It is not necessary to solve the equation.Assume that interest is at the rate of 10% compounded semiannually.

A man bought a stereo system for $3500 and agreed to pay off the loan by making monthly payments of $79.If the store charges an interest rate of 11% compounded monthly,how many months will it take to pay off the debt?

At what nominal rate of interest,compounded monthly,will an investment double in 15 years?

Find the present value of an ordinary annuity with monthly payments of $125 for 10 years at 4.5% compounded monthly.

Find the future value of an annuity due with quarterly payments of $550 for 32 years at 3.75% compounded quarterly.

Miguel has the opportunity to invest $3000 in a friend's business such that he will be repaid $4500 in six years.If he instead wanted to put the $3000 into a savings account,what interest rate compounded monthly would be needed to equal the investment?

Suppose you wish to purchase a factory that will yield an annual return of $12,000 for 12 years,after which the factory will have no value.You want to earn 8.25% annually on your investment and also set up a sinking fund to replace the purchase price.If money is placed in the fund at the end of each year and earns 4.2% compounded annually,how much should you pay for the factory?

Find the present value of $300 due after six years if the interest rate is 5.4% compounded monthly.

A trust fund for a 8-year-old child is being set up by a single payment so that when the child is 20 there will be $12,000.If the fund earns interest at the rate of 6.5% compounded semiannually,how much money should be paid into the fund initially?

A ball rebounds of its previous height after each bounce.If the ball is dropped from a height of 27 feet,how far has it traveled in the air when it hits the ground for the twentieth time?

Find the present value of an ordinary annuity with quarterly payments of $250 for 40 years at 7.25% compounded quarterly.

Suppose you have the opportunity to invest $1000 in a business such that the value of your investment after seven years will be $1500.On the other hand,you can put the $1000 into a certificate of deposit that pays 6% compounded monthly.Which is better?

Find the sum of the geometric series: 1 + 2 + + ...+

If an initial investment of $4000 grows to $4884 in five years,find the nominal rate of interest,compounded monthly,that was earned by the money.

If $3,100 is invested at a nominal rate of 6% compounded quarterly for 7 years,find a)the compound amount,and b)the compound interest.

At what nominal rate of interest,compounded quarterly,will money double in 10 years?