Exam 6: Mathematics of Finance

Consider the following annuity: $2000 due at the end of each year for two years,and $3000 due thereafter at the end of each year for three years.At an interest rate of 4% compounded annually,the present value of the annuity is

A company repays a $50,000 loan by paying 10% of the outstanding loan each month.How much has the company paid back after two years?

If $200 is deposited into a savings account that earns interest at an annual rate of 8% compounded continuously,find the value of the account at the end of two years.

After graduating from college and gaining employment,you decide to open an IRA to help save for retirement.If the IRA earns 6.15% compounded monthly and you deposit $250 into this IRA at the end of each month,what will be the amount you have when you retire 43 years later?

Suppose that you can invest $10,000 in a business that guarantees you the following cash flows: $5000 at the end of 2 years,$4000 at the end of 4 years,and $3000 at the end of 6 years.Assuming an interest rate of 7.25% compounded annually,find the net present value of the cash flows.Is the investment profitable?

If $5000 is used to purchase an annuity consisting of equal payments at the end of each month for the next and the interest rate is 6% compounded monthly,find the amount of each payment.

Suppose you wish to purchase a mine that will yield an annual return of $32,000 for 12 years,after which the mine will have no value.You want to earn 8% annually on this 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 6.2% compounded annually,how much should you pay for the mine?

What is the effective rate that corresponds to a nominal rate of 20% compounded quarterly?

A house worth $150,000 ten years ago has increased in value at an effective rate of 3% due to inflation.Find the current value of the home.

Suppose you deposit $200 at the beginning of every month into a bank account that pays 6% compounded monthly.After six years,how much will you have?

How much must be invested at an interest rate of 9.6% compounded monthly to have $3000 in five years?

If $1000 is deposited into a savings account that earns interest at an annual rate of 6% compounded continuously,find the value of the account at the end of seven years.Give your answer to the nearest dollar.

Cyndi bought a multimedia home computer system for $4500 and agreed to pay off the loan by making monthly payments of $109.If the store charges an interest rate of 9.7% compounded monthly,how many months will it take to pay off the debt?

A person establishes the following retirement plan: an immediate deposit of $10,000 and quarterly payments of $1,500 at the end of each quarter into a savings account that earns 5% compounded quarterly,what is the amount of the investment after 21 years?

A bank charges 0.5 % service fee on checking accounts.If $ 1,000 was deposited in such account,use the concept of negative interest rate to find an approximate value of the amount in this account after 10 years.

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

A woman makes house payments of $4200 at the beginning of every quarter.If the woman wishes to pay worth of payments in advance,how much should she pay provided that the interest rate is 5.4% compounded quarterly?

An interest rate of 8% compounded semiannually corresponds to an effective rate of

A company repays a $50,000 loan by paying 10% of the outstanding loan each month.Find the amount the company pays in the fourth and twentieth months.