Exam 6: Mathematics of Finance

A person amortizes a loan of $180,000 for a new home by obtaining a 30-year mortgage at the rate of 8.7% compounded monthly.Find (a)the monthly payment,(b)the total interest charges,and (c)the principal remaining after 10 years.

A $5000 loan is to be repaid over three years by equal payments due at the end of every quarter.If interest is at the rate of 20% compounded quarterly,determine (a)the quarterly payment and (b)the total interest paid.

If $5,600 is invested at an effective rate of 2.1% for 17 years,what is the compound amount?

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 15 years with an interest rate of 8% compounded monthly.

A couple bought a motorboat for $11,000 and agreed to pay off the loan by making monthly payments of $559.If the dealer charges an interest rate of 8.9% compounded monthly,how many months will it take to pay off the debt?

Suppose an initial investment grows from $220 to $600 over fifteen years.First find the nominal rate compounded monthly and then find the equivalent effective rate.

The population of a city grows from 110,000 to 116,600 in one year.If the city continues to grow at that rate,find the number of years it will take for the population to double.

At an annual rate of 4% compounded continuously,in how many years would it take for a principal to double?

Suppose a machine costing $12,000 is to be replaced at the end of 7 years,at which time it will have a salvage value of $6000.In order to provide money at that time for a new machine costing $15,000,a sinking fund is set up into which equal payments are placed at the end of every quarter.If the fund earns 5.6% compounded quarterly,what should each payment be?

If $4,200 is invested at an annual rate of 5.4% compounded monthly for 10 years,find the compound amount.

How many years will it take for a principal to double at a rate of 10% compounded annually? Give your answer to the nearest year.

A company earns a profit of $5000 in its first month.Suppose its profit decreases by 10% each month for one year.Find the amount of profit the company earns in its first year.

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 $1500 at the end of 6 years.Use a graphing calculator to graph the net present value as a function of the interest rate compounded annually.Determine the interest rate for which the investment is profitable.

Find the amount of an annuity of payments of $150 at the end of every month for 3 years at the rate of 4% compounded monthly.Also find the compound interest.

At an annual rate of 8% compounded continuously,in how many years would it take for a principal to double?

If a person deposits $1000 in a savings account that pays an interest rate of r% compounded continuously,and the account has $1400 at the end of 4 years,find the interest rate.

Find the present value of a future value of $5,000 due in 7 years at a nominal rate of 3% compounded quarterly.

Find the future value of an ordinary annuity with quarterly payments of $300 for 30 years at 7.5% compounded quarterly.

Suppose a diagnostic machine will yield a net of $1000 per quarter for 5 years,after which the machine can be sold for $1000.How much should a firm pay for the machine if it wants to earn 7.5% annually on its investment and also set up a sinking fund to replace the purchase price? For the fund,assume quarterly payments and a rate of 5.5% compounded quarterly.