Exam 6: Mathematics of Finance

Suppose $500 is initially placed in a savings account that earns interest at the rate of 8% compounded semiannually.Thereafter,$500 is deposited in the account at the end of every six months for five years.The value of the account at the end of five years is

At what nominal rate of interest,compounded quarterly,will an investment double in 15 years?

James amortizes a loan of $210,000 for a new home by obtaining a 40-year mortgage at the rate of 7.5% compounded monthly.Find (a)the monthly payment,(b)the total interest charges,and (c)the principal remaining after 15 years.

At a car dealership,you are given two options for financing a new car worth $16,000.Option 1:You can take out a 5 year loan at 0% A.P.R.compounded monthly,or Option 2: You can get $3,000 cash back and finance the rest at 4.9% A.P.R.compounded monthly for 5 years.Which is the better option for you?

Find the future value of an annuity due consisting of payments of $100 paid at the beginning of each quarter for five years at the rate of 5% compounded quarterly.

A company repays a $40,000 loan by paying 20% of the outstanding loan every four months for five years and then pays off the rest.How much was the company's final payment?

Determine the effective rate equivalent to an annual rate of 8% compounded continuously.

What is the present value of an annuity of $300 per quarter for five years at an interest rate of 4.5% compounded quarterly?

Find the sum of the geometric series: 1 + + + +

A trust fund for a child's education is being set up by a single payment so that at the end of 17 years there will be $31,000.If the fund earns interest at the rate of 8.25% compounded monthly,how much money should be paid into the fund initially?

Find the present value of an annuity due with quarterly payments of $2,750 for 27 years at 7.8% compounded quarterly.

An investment grows from $5500 to $6105 in one year.If the investment continues to grow at that rate,find the number of years it will take for the investment to triple.

If $12,000 is used to purchase an annuity consisting of equal payments at the end of every six months for the next 7 years and the interest rate is 6.2% compounded semiannually,find the amount of each payment.

Given an interest rate of 7.25% compounded monthly,find the present value of the following annuity: $700 at the end of each month for three years and $900 at the end of each month for five more years.

The population of a small town is growing at an effective rate of 2.1%.If the current population is 53,000,what will the population be in 8 years?

A debt of $600 is due 3 years from now and $800 due 5 years from now,is instead to be paid off by two payments: $500 now and a final payment at the end of 6 years.What would this payment be if an interest rate of 6% compounded quarterly is assumed?

$200 is invested at the rate of 3.5% compounded quarterly for six and a half years.How many terms are in the geometric sequence formed by the amounts at the end of each quarter?

Mary amortizes a loan of $80,000 for a new home by obtaining a 15-year mortgage at the rate of 9.9% compounded monthly.Find (a)the monthly payment,(b)the total interest charges,and (c)the principal remaining after 8 years.

Given an annuity with equal payments at the end of each month for six years and an interest rate of 5.3% compounded monthly,use a graphing calculator to graph the present value A as a function of the monthly payment R.Determine the monthly payment if the present value of the annuity is $30,000.

An investment grows from $600 to $642 in one year.If the investment continues to grow at that rate,find the number of years it will take for the investment to double.