Exam 6: Mathematics of Finance

If $2,575 is invested at an A.P.R.of 7% compounded semiannually for 15 years,find the accumulated amount.

A ball rebounds of its previous height after each bounce.If the ball is tossed up to a height of 16 feet,how far has it traveled in the air when it hits the ground for the fifteenth time?

The Krishnans amortize a loan of $150,000 for a new home by obtaining a 40-year mortgage at the rate of 10.2% compounded monthly.Find (a)the monthly payment,(b)the total interest charges,and (c)the principal remaining after 15 years.

A trust fund for a 12-year-old child is being set up by a single payment so that when the child is 21 there will be $24,000.If the fund earns interest at the rate of 7.25% compounded quarterly,how much money should be paid into the fund initially?

Suppose a person invests $20,000 in a business venture that guarantees the same cash flow at the end of every quarter for four years.If the investment earns interest at the rate of 16% compounded quarterly,then each cash flow is

If $30,000 is used to purchase an annuity consisting of equal payments at the end of each quarter for the next 5 years and the interest rate is 8% compounded quarterly,find the amount of each payment.

Suppose a machine will yield a net of $200 per month for 5 years,after which the machine would be worthless.How much should the firm pay for the machine if it wants to earn 5% annually on its investment and also set up a sinking fund to replace the purchase price? For the fund,assume monthly payments and a rate of 4% annually.

Suppose an initial investment grows from $12,000 to $30,000 over ten years.First find the nominal rate compounded quarterly and then find the equivalent effective rate.

Find the future value of an ordinary annuity with semiannual payments of $475 for 30 years at 6.15% compounded semiannually.

If $10,000 is invested at an effective rate of 4.25% for 8 years,what is the accumulated amount?

= 6,r = 5

$200 is invested at the rate of 6% compounded monthly for 5 months.List the compound amounts at the end of each month as a geometric sequence.

Suppose that you want to invest some money in order to have $1000 available at some later time.If you invest it at 7% interest compounded continuously,the amount you need to invest now,P,is related to the number of years from now that you need the money,t,by: P(t)= 1000 .Graph this on your graphing calculator in the window × .Discuss the behavior of this graph.

A trust fund is to be established by a single payment so that at the end of 15 years,there will be $20,000 in the fund.If the fund earns interest at the rate of 8% compounded semiannually,how much should be deposited initially into the fund?

Suppose that you want to invest some money in order to have $100 available at some later time.If you invest it at 7% interest compounded continuously,the amount you need to invest now,P,is related to the number of years from now that you need the money,t,by: P(t)= 100 .Graph this on your graphing calculator in the window × Discuss the behavior of this graph.

At an annual rate of 10% compounded continuously,the number of years in which a principal triples is

Given that the effective rate is 9%,determine the interest rate r which is compounded continuously to give an effective rate of 9%.

Find the present value of $5000 due in 3 years if the interest rate is % compounded monthly.

Suppose an annuity due consists of 6 yearly payments of $200 and the interest rate is 5% compounded annually.Determine (a)the present value and (b)the future value at the end of 6 years.