Exam 3: The Time Value of Money: An Introduction to Financial Mathematics

Suppose you deposited $250 at the end of 2011,2012,2013 and 2014.How much would you have in your account on 1 January 2015,based on annual compounding of 8% by your bank?

Calculate the present value of a government security that promises to pay $100 p.a.forever,assuming an interest rate of 11% per annum.

An annuity in which the first cash flow is to occur after a time period that exceeds the time period between each subsequent cash flow is known as a/an:

Assume that you will require $1000 in four years' time.Suppose that you can afford to deposit only $186.29 at the end of each year,the first deposit to be made in one year's time.What interest rate would you require to reach your target if the bank compounds annually?

You have borrowed $1000 from a friend to pay for unforeseen car repairs,with an agreement to pay interest at an annual rate of 18%,compounding daily.If you repaid your friend after 90 days,how much would you need to repay?

The nominal interest rate is difference between the inflation rate and the real rate of interest.

An individual borrowed $100 000 at a fixed interest rate of 12% p.a.for the entire loan term of 20 years.If the loan is to be repaid through equal monthly instalments,then the regular repayment to the nearest dollar is $1101.

You have borrowed $300 000 over 30 years in order to purchase your first home.The loan repayments are monthly at a nominal interest rate of 6.5% per annum compounded monthly. a.What are the repayments? b.If after two years the interest rate rises to 7.5% per annum what are the new monthly repayments? c.If the interest rate does not change but from the beginning you decide to repay $2500 per month how long will it take to repay the loan? What amount would be the final repayment?

A process by which,through the operation of interest,a present sum becomes a greater sum in the future is:

Calculate the value of an investment at the end of its fourth year if the initial investment is $10 000 and it produces the following annual rates of return: Year 1,gain 15%;Year 2,gain 17%;Year 3,loss 5%;Year 4,gain 4%.

Debt Ltd borrowed $100 000 from its local bank to finance the purchase of new equipment.Annual payments are required over five years at a fixed interest rate of 10% p.a.How much is each annual payment?

Assume that on 1 January 2011 you deposit $1000 into a savings account that pays 8% p.a.If the bank compounds interest quarterly,how much will you have in your account on 1 January 2014?

An individual is offered the sum of $100 000 to be received after 5 years.If the relevant interest rate is 8% p.a. ,compounding annually,then the present value of this promised sum is $68 058.32.

Assume that on 1 January 2011 you deposit $1000 into a savings account that pays 8% p.a.If the bank compounds interest annually,how much will you have in your account on 1 January 2014?

The rate of return can be shown as:

If you invest $47 000 for five years at 9.7% p.a.(interest paid annually and then reinvested),what is the value of your investment at the end of the five-year period?

The amount that corresponds to today's value of a promised future sum can be shown as:

You have an outstanding car loan of $300 per month for the next 2 years.As you are finishing your studies this year,it would be better if you could pay the full sum at the end of two years.If the interest rate on the loan is 6% per annum (compounded monthly),what final sum would the bank require at the end of two years so that it is indifferent between the two methods of payment?

Continuous interest rates are an example of where the future sum grows _____________.

You have $10 000 to invest.If you invest it at 11.2% p.a.for six months,then invest the initial $10 000 together with any interest for a further 12 months at 12.7% p.a. ,what will be the value of your investment at the end of the 18-month period?