Finance 450 LS 4, 5,

Given an annuity that has a payment of $35 per year, an annual interest rate of 3%, and a present value of $130, it will last for ___ years

35[{1-(1+.03)^-n}/.03]= 4

More frequent compounding leads to:

Higher EARs

Calculating the present value of a future cash flow to determine its worth today is commonly called ____ valuation

discounted cash flow

The current value of a future cash flow discounted at the appropriate rate is called the ___ value.

present

Which of the following is the general formula for the EAR when m is the number of times interest is compounded in a year?

(1 + quoted rate / m) ^m - 1

If you invest for a single period at an interest rate of r, your money will grow to ___ per dollar invested.

(1 +r)

Suppose you paid a $1,200 loan off by paying $400 in principal each year plus 10% yearly interest. How much is the 2nd interest payment?

(1,200-400) x .1 = $80

If the quoted interest rate is 2% per month (APR=24%), what is the EAR?

(1.02)^12-1= 126.82%

A credit card charges 18% interest per year (APR) (1.5% each month). What is the EAR?

(1.05)^12-1 = 19.56%

If the future value factor for$1 invested for 5 years at 10% is ___, then the corresponding present value factor for $1 received in 5 years with a 10% discount rate is ___.

1.611; 0.6209

The present value interest factor for $1 at 5% compounded annually for 5 years is:

1/(1.05)^5= 0.7835

The future value of an annuity due of $100 per year for 10 years at 10% per year is:

100[(1.10^10-1)/0.10][1.10]= $1,753.12

The interest rate charged per period multiplied by the number of periods per year is the ___ ___ ___

Annual percentage rate

To calculate the future value of $100 invested for t years at r interest rate, you enter the present value in your calculator as a negative number. Why?

Because the $100 is an outflow from you which should be negative

The effective annual rate (EAR) takes into account the ___ of interest that occurs within a year.

Compounding

Which of the following is the appropriate Excel function to convert a quoted rate of 12% compounded quarterly to an EAR?

EFFECT(0.12,4)

If you invest $100 for 5 years at 10% interest compounded annually, which of the following will be the formula for the future value of your investment?

FV=100x(1.1)^5

T or F: Future value refers to the amount of money an investment is worth today

False

The amount an investment is worth after one or more periods is called the ___ value.

Future

Why is a dollar received today worth more than a dollar received in the future?

Inflation will make a dollar in the future worth less than a dollar today and today's dollar can be reinvested, yielding a greater amount in the future

The entire principal of an interest-only loan is the:

Original loan amount

The basic present value equation is:

PV= FVt/(1+r)^t

If FV=PV x (1+r) is the single period formula for future value, which of the following is the single period present value formula?

PV=FV/(1+r)

Suppose you expect to receive $5,000 in one year, $4,300 more in two years, and an additional $5,000 in three years. Match present value amount to the corresponding cash flow assuming a discount rate of 17%.

Present value of the year 1 cash flow= 5,000/1.17= 4,273.5 Present value of the year 2 cash flow= 4,300/(1.17)^2=3,141.21 Present value of the year 3 cash flow= 5,000/(1.17)^3= 3,121.85

T or F: when calculating the present value of an annuity using the financial calculator, you end the cash flows of the annuity in the PMT key

True

The first cash flow oat the end of week 1 is $100, the second cash flow at the end of month 2 is $100, and the third cash flow at the end of year 3 is $100. This cash flow pattern is a(n) ___ type of cash flow.

Uneven

You invest $500 at 10% interest per annum. At the end of 2 years with simple interest you will have ___ and with compound interest you will have ___. simple=500(0.10)=$50 per year times 2 years = $100 adding original =$600 compound=500(1.10)^2=605

$600; $605

Time value of money tables are not as common as they once were because:

It is easier to use inexpensive financial calculators instead and they are available for only a relatively small number of interest rates.

The formula for the present value of an annuity due is:

(1+r) x (PV of an ordinary annuity)

An investment offers a perpetual cash flow of $100 every year. The required return on this investment is 10%. Which of the following is the value of this investment?

100/.1= $1,000

You agree to repay $1,200 in 2 weeks for a $1,000 payday loan. What is your EAR assuming that there are 52 weeks in a year?

11,347.55%

If a firm's sales are growing at 5% per year, how long will it take for the firm's sales to triple?

22.5

The process of accumulating interest in an investment over time to earn more interest is called ___

Compounding

Amortization is the process of paying off loans by regularly reducing the ___.

Principal

Which of the following is the simplest form of loan?

Pure discount loan

The difference between the present value of an ordinary annuity with payments of $100 per year at 10% compounded annually for 10 years and an annuity due with payments of $100 per year at 10% compounded annually for 10 years is:

The difference is PV(annuity due - PV(ordinary annuity), or $675.90-$614.46= $61.45

Which of the following can be used to calculate present value?

an algebraic function, a time value of money table, and a financial calculator

Which of the following are ways to amortize a loan?

Pay principal and interest every period in a fixed payment & pay the interest each period plus some fixed amount of the principal

The real world has moved away from using ____ for calculating future and present values.

time value of money tables

Because of ___ and ___, interest rates are often quoted in many different ways

tradition; legislation

The future value of $100 compounded for 50 years at 10% per year is:

$11,739.09

The future value of $100 investment in 4 years compounded at 8% per year equals ___.

$136.05

What is the present value of an annuity that pays $100 per year for 3 years if the interest rate is 10% per year

$248.69

If you invest $500 for one year at a rate of 8% per year, how much interest will you earn?

$40

For a given time period (t) and interest rate (r), the present value factor is ___ the future value factor.

1 divided by and the reciprocal of

You must invest ___ today at 8% to get $2 in one year.

1.85

If the quoted interest rate is 2% per month (12 months in a year), what is the APR?

24% = 2%/month x 12 months

How long will it take $40 to grow to $240 at an interest rate of 6.53% compounded annually?

28.33

Suppose you paid off a $1,200 loan by paying $400 in principal each year plus 10 % annual interest over a 3 year period. What is the total payments (interest plus principal) in Year 3?

400 + (1200-800) x .1 = 440

The present value interest factor for an annuity with an interest rate of 8% per year of 20 years is ___.

9.8181

Which of the following is the correct Excel function to calculate the present value of $300 due in 5 years at discount rate of 10%?

=PV(0.10,5,0,300)

In the excel setup of a loan amortization problem, which of the following occurs?

To find the principal payment each month, you subtract the dollar interest payment from the fixed payment. The payment is found with =PMT(rate, nper, -pv, fv)

T or F: The formula for a present value factor is 1/(1+r)^t

True

A perpetuity is a constant stream of cash flows for a(n) ___ period of time

infinite

When finding the present or future value of an annuity using a financial calculator, the ___ ___ should be entered as a percentage.

interest rate

An ordinary annuity consists of a(n) ___ stream of cash flows for a fixed period of time.

level

Given an investment amount and a set rate of interest, the ___ the time period, the ___ the future value.

longer; greater

The concept of the time value of money is based on the principle that a dollar today is worth ___ a dollar promised at some time in the future.

more than

Which of the following are real-world examples of annuities?

pensions, leases, mortgages

Suppose you borrow $1,000 at 5% interest per year for 10 years. The loan is an interest only loan so each year you will pay ____.

$50 = 5%x$1,000

What is the future value of $100 deposited each year for 2 years beginning next year, then $200 deposited for the next 2 years if you can earn 6% per year?

$643.46

When entering variable in an Excel function (or in a financial calculator) the "sign convention" can be critical to achieving a correct answer. The sign convention says that outflows are negative values; inflows are positive values. For which variables is this a consideration?

-payment -present value -future value

Using a time value of money table,w hat is the future value interest factor for 10% for 2 years?

1.21

Suppose we invest $100 now and receive $259.37 in 10 years. What rate of interest will we achieve?

10%

Ralph has $1,000 in an account that pays 10% per year. Ralph wants to give his money to his favorite charity by making 3 equal donations at then end of the next 3 years. How much will Ralph give to the charity each year?

1000/[(1-1/1.10^3)/0.10= $402.11

The correct future value interest factor in a time value of money table for finding the future value of $100 in 10 years at 10% per year interest is ___.

2.5937

You plan to deposit $100 per year for the next 10 years, in an account paying 8%. How much will you have in this annuity?

=FV(0.08,10,-100,0)

An annuity with payments beginning immediately rather than at the end of the period is called an ___.

annuity due

In almost all multiple cash flow calculations, it is implicitly assumed that the cash flows occur at the ___ of each period.

end

Which of the following are the primary ways used to perform financial calculations today?

financial calculator and spreadsheet functions

The formula for the ___ value interest factor of an annuity is: [1-1/(1+r)^t]/r

present

With discounting, the resulting value is called the ___ value; while with compounding the result is called the ___ value.

present; future

The original amount of a loan is termed the loan ___.

principal

What typical interest only loans, the entire principal is:

repaid at some point in the future

An interest rate expressed in terms of the interest payment made each period is called a(n) ___.

stated interest rate & quoted interest rate

C/r is the formula for the present value of a(n) ___.

Perpetuity

T or F: the formula for the future value of an annuity factor is [(1+r)^t-1]/r

True