Exam 6: Mathematics of Finance

Suppose the Laus wish to save $36,000 for a down payment in three years.If they make payments at the end of every month into an account paying 7.5% compounded monthly,what size payments should they make?

$50,000 per year at the rate of 10% yearly

Suppose you invest an initial amount of $10,000 at an annual rate of 8.2% compounded monthly.Use a graphing calculator to graph the compound amount S as a function of the interest periods.Determine how long it takes for the investment to accumulate to $22,500.

In order to establish a sinking fund of $125,000,how much will have to be invested at the end of each year at the rate of 11.2% compounded annually for 8 years?

Find the present value of a future value of $4,200 due in 11 years at a nominal rate of 6% compounded monthly.

A ball rebounds of its previous height after each bounce.If the ball is dropped from a height of 20 meters,how far has it traveled in the air when it hits the ground for the sixth time?

Suppose you have the opportunity to invest $6000 in a business venture such that you will be repaid $8000 in five years.On the other hand,you can put the $6000 in a savings account that pays 5.25% compounded monthly.Which investment is better?

If an initial investment of $4000 grows to $5718 in six years,find the nominal rate of interest,compounded quarterly,that was earned by the money.

Find the amount of an annuity consisting of payments of $100 paid at the end of each quarter for five years at the rate of 5% compounded quarterly.Also find the compound interest.

To purchase land for an industrial site,a company agrees to pay $20,000 down and $10,000 at the end of every six-month period for 10 years.If the interest rate is 10% compounded semiannually,what is the corresponding cash value of the land?

A trust fund is to be set up by a single payment so that at the end of 10 years there will be $1,000,000 in the fund.If interest is compounded continuously at an annual rate of 9%,to the nearest dollar,how much money should be paid into the fund initially?

Suppose you leave an initial amount of $250 in a savings account for 20 years.If interest is compounded daily (use 365 times per year),use a graphing calculator to graph the compound amount S as a function of the nominal rate of interest.Determine the nominal rate of interest so that the amount doubles after 20 years.

Given a payment of $800 per quarter for five years,use a graphing calculator to graph the present value A as a function of the interest rate per quarter r.Determine the nominal interest rate if the present value of the annuity is $14,000.

The premiums on an insurance policy are $80 every six months,payable at the beginning of each six-month period.If the policy holder wishes to pay 1 year's premiums in advance,how much should be paid provided that the interest rate is 4.3% compounded semiannually?

How much must be invested at an interest rate of 7.25% compounded quarterly to have $10,000 in two years?

You have a choice of two banks.One bank pays interest at 5.54% compounded monthly and the other bank pays interest at 5.53% compounded daily (365 times a year).Which is the better choice? How much more would you make in one year if you deposited $1000?

The function that gives the effective rate that corresponds to an annual rate of x interest compounded continuously is y = - 1.Graph this on your graphing calculator in the window × and discuss what the behavior means.

Find the present value of a future value of $4,650 due in 18 months at an effective rate of 4.55%.

Find the present value of an annuity due with semiannual payments of $350 for 35 years at 6.25% compounded semiannually.

Suppose that Tori can invest $13,000 in a business that guarantees her the following cash flows: $6000 at the end of 2 years,$5000 at the end of 4 years,and $4000 at the end of 6 years.Assuming an interest rate of 6% compounded monthly,find the present value of the cash flows.Is the investment profitable?