Exam 6: Mathematics of Finance

An investment grows from $10,240 to $10,700.80 in one year.If the investment continues to grow at that rate,find the number of years it will take the investment to double.

A person deposits $1000 in a savings account that pays an interest rate of % compounded continuously.Find the balance in the account at the end of years.

$200 is invested at the rate of 4.5% compounded semiannually for 8 years.Find the compound amounts at the end of the 2nd,4th,and 8th years.

Find the future value of an annuity due with monthly payments of $250 for 26 years at 6% compounded monthly.

A person purchases a home for $130,000,makes a down payment of $30,000.Find the monthly payment if the person takes a loan for 25 years with an interest rate of 8% compounded monthly.

Suppose you leave an initial amount of $320 in a savings account for 30 years.If interest is compounded monthly,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 triples after 30 years.

An investment is growing at an effective rate of 12.4%.If the amount invested is currently $12,000,what will the amount be in 6 years?

Suppose that you can invest $8000 in a business that guarantees you the following cash flows: $4000 at the end of 2 years,$3500 at the end of 4 years,and $2000 at the end of 7 years.Use a graphing calculator to graph the net present value as a function of the interest rate compounded annually.Determine the interest rates for which the investment is profitable.

To what sum will $1000 accumulate if it is invested at 10% compounded annually for one year and then at 10% compounded semiannually for two years?

A debt of $2000 due four years from now is to be repaid by a payment of $1000 now and a second payment at the end of two years.How much should the second payment be if the interest rate is 5% compounded annually?

A man purchased a new laser printer for his computer for $1100 and agreed to pay off the loan by making monthly payments of $59.If the store charges an interest rate of 12.2% compounded monthly,how many months will it take to pay off the debt?

Find the present value of $3000 due after five years if the interest rate is 9.6% compounded semiannually.

An investment is compounded daily (use 365 times per year).Use a graphing calculator to graph the effective rate, ,as a function of the nominal rate r.Then use the graph to find the nominal rate that is equivalent to an effective rate of 5.4%.

You wish to be a millionaire when you retire.To accomplish this you decide to open up an IRA and make equal monthly payments at the end of each month.If the IRA earns 7.5% compounded monthly and you know you will retire in 40 years,what must be the monthly payment to obtain your $1,000,000?

If $100 is invested at a rate of 6% compounded continuously,the amount in the account is given by: S = .If the principal is invested at an account earning 6% compounded monthly,the amount is given by: S = 100 ∙ .Consider the difference in these two investments by graphing both functions on your graphing calculator and looking at the years 5 through 6.(Use the window × .)What do you notice about the two graphs?

Suppose that you can invest $5000 in a business that guarantees you the following cash flows: $3000 at the end of 2 years,$2000 at the end of 4 years,and $2000 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?

Suppose that you can invest $11,000 in a business that guarantees you the following cash flows: $5500 at the end of 2 years,$4500 at the end of 4 years,and $4000 at the end of 5 years.Assuming an interest rate of 6.25% compounded annually,find the net present value of the cash flows.Is the investment profitable?

A debt of $12,000,which is due 10 years from now,is instead to be paid off by four payments: $3000 now,$2000 in 3 years,$2000 in 6 years,and a final payment at the end of 8 years.What would this payment be if an interest rate of 5.5% compounded semiannually is assumed?

Suppose an initial investment grows from $2000 to $2817.39 over three years.First find the nominal rate compounded monthly and then find the equivalent effective rate.

An initial investment of $2600 grows at an annual rate of 7.5% compounded monthly.Find how long it takes for the investment to amount to $3500.