CISC 121 Lecture Notes - Lecture 10: Life Annuity, Life Insurance, Random Variable

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20 Oct 2018

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Immediate annuity: a n = (1 v n)/i. While life insurance provides payment to a beneficiary in the event of death, life annuities provide income dependent upon survival of the annuitant. There are various payment patterns, but we will restrict ourselves to annuities that pay once a year (discrete annuities). As you may remember from math 384, a series of annual payments may begin now (annuity due) or a year from now (immediate annuity). Annuity due: n = (1 v n)/d. These two annuities above will make n payments with absolute certainty. Life annuities, however, will make an uncertain number of payments. The present value random variable of a life annuity is y, and so the actuarial present value is then e[y]. The formulas provided will be for a unit amount of per year, but if you want a different value, just multiply both sides as was done with the life insurance formulas.

Related Questions

Question 1 5 pts

0 multiple_choice_question 22046808

The internal rate of return (IRR) is the interest rate that sets the net present value of the future cash flows equal to ________.

Question 2 5 pts

On a timeline, the space between date 0 and date 1 represents the _______ between dates. Letâs assume it is the first year of the loan. Date 0 is the beginning of the first year, and date 1 is the end of the first year.

Question 3 5 pts

As the interest rate __________, present value decreases.

Question 4 5 pts

The present value (PV) of a stream of cash flows is the _______ the present values of each individual cash flow

Question 5 5 pts

When a constant cash flow will occur at regular intervals for a finite number of periods of time, it is called a(n) __________.

Question 6 5 pts

Edit this Question Delete this Question

0 multiple_choice_question 22047052

There are two basic types of annuities:

Discounted and compounded annuities

Ordinary annuities and annuities due.

Future value and present value annuities

None of the above

Question 7 5 pts

The NPV measures the ______ change in shareholder wealth that arises from undertaking a project.

Question 8 5 pts

The Net Present Value rule implies that we should compare a projectâs net present value (NPV) to ________

Question 9 5 pts

To endow a perpetuity is the same as calculating the present value (PV) of a perpetuity. Say you want to endow an annual graduation party at your alma mater. You want the event to be a memorable one, so you budget $30,000 per year forever for the party. If the university earns 8% per year on its investments, and if the first party is in one yearâs time, how much will you need to donate to endow the party?

The formula for PV of a perpetuity = C\r; = $30,000 \ 0.08; =

Question 10 5 pts

With an Ordinary Annuity, payments are required at the ________ of each period. An example of this is bonds which usually pay coupon payments at the end of every six months until the bond's maturity date.

beginning

middle

end

payments are not required

limemacaw827

Question 1 of 25

You are planning to deposit $1,000 in a savings account. Account A compounds semiannually while account B compounds monthly. If both accounts have the same quoted annual rate of interest, you should choose _______________.

A. either account since both quote the same rate of interest

B. account A because it has a higher APR

C. account A because it has a higher EAR

D. account B because it is compounded more often

Question 2 of 25

You are evaluating two annuities. They are identical in every way, except that one is an ordinary annuity and the other is an annuity due. Which of the following is FALSE?

A. The ordinary annuity must have a lower future value than the annuity due.

B. The ordinary annuity must have a higher present value than the annuity due.

C. The two annuities will differ in present value by the amount (1+r).

D. The annuity due and the ordinary annuity will make the same number of total payments over time.

Question 3 of 25

What is the total present value of $80 received in one year, $300 received in two years, and $700 received in six years if the discount rate is 7%? Note: There is no direct formula for this kind of PV computation other than the basic equation, PV = FV/(1+r)t. 0 1 2 3 4 5 6 |-----------|----------|----------|----------|----------|---------| PV=? $80 $300 $700

A. $582.72

B. $681.68

C. $757.25

D. $803.24

Question 4 of 25

You need to borrow $23,000 to buy a car. The current loan rate is 7.9% APR compounded monthly and you want to pay the loan off in equal monthly payments over 5 years. What is the correct computation to find your monthly payment (C)?

A. C = $23,000 [PVIFA(7.9%/12, 60)]

B. $23,000 = C [1 - (1/1.0795)] / .079

C. $23,000 = C [1 - (1 /1.0065860)] / .00658

D. C = $23,000 [1 - (1/1.07960)] / .079

Question 5 of 25

The monthly mortgage payment on your house is $821.69. It is a 30-year mortgage at an APR of 6.5% compounded monthly. How much did you borrow? Note: PVIFA(r, t) = [1 â 1/(1+r)t] / r, and of course, you can use your calculator here.

A. $100,000

B. $115,000

C. $130,000

D. $140,000

Question 6 of 25

You just won the lottery and you are given two choices for your prize money: (1) A present lump sum of $20 million or (2) $1 million per year that you and your heirs will receive forever, beginning one year from now. If the appropriate interest rate is 5%, which should you choose and why? Note: PV of a perpetuity = C/r

A. Either, because both have the same present value.

B. (1) because it has a higher present value.

C. (2) because it has a higher present value.

D. (2) because it has a higher future value.

Question 7 of 25

What is the effective annual rate of 6% compounded quarterly? Note: EAR = (1 + APR/m)m â 1.0, where m is the number of compoundings in a year.

A. 6.00%

B. 6.14%

C. 7.50%

D. 24.00%

Question 8 of 25

At the end of each year for the next 8 years you will receive cash flows of $500. The initial investment is $2,500. Which of the following is the correct equation to find the rate of return (r) you are expecting from this investment?

A. $2,500 = $500 [1/(1+r)8 â 1] / r

B. $500 = $2,500 [PVIFA(r%,8)]

C. $500 = $2,500 [FVIFA(r%,8)]

D. $2,500 = $500 [1 â 1/(1+r)8] / r

Question 9 of 25

Consider the following cash flow stream. What is the correct way to find the present value of this cash flow stream at a 10% discount rate? 0 1 2 3 4 5 6 7 8 9 10 |----------|----------|----------|----------|----------|----------|---------|----------|----------|----------| PV=? $35 $35 $35 $35 $35 $35 $20 $20 $20 $20

A. PV = 35 [PVIFA(10%, 6)] + 20 [PVIFA(10%, 4)]

B. PV = 20 [PVIFA(10%, 10)] + 15 [PVIFA(10%, 6)]

C. PV = 35 [PVIFA(10%, 10)] â 15 [PVIFA(10%, 4)]

D. PV = 35 [PVIFA(10%, 6)]/(1.10)6 + 20 [PVIFA(10%, 4)]

Question 10 of 25

You plan to amortize your $10,000 loan by making five equal payments over the next 5 years. The interest rate is 5% compounded annually. What number should appear in (A) of your amortization table below? Note: PVIFA(5%, 5)=4.3295.

Beginning Ending Year Loan Balance Payment Interest Principal Loan Balance

----------------------------------------------------------------------------------------------

1 $10,000 xxxx xxx xxx xxxx

2 ( A ) xxxx xxx xxx xxxx

3 xxxx xxxx xxx xxx xxxx

4 xxxx xxxx xxx xxx xxxx

5 xxxx xxxx xxx xxx 0

A. $8,457.12

B. $8,190.26

C. $7,690.26

D. $6,809.74

Question 11 of 25

The rate of return required by investors for owning a bond to its maturity is called the

A. coupon rate.

B. current yield.

C. dividend yield.

D. yield to maturity.

Question 12 of 25

Which of the following statements regarding bond terminologies is INCORRECT?

A. The written, legally binding agreement between the corporate borrower and the lender detailing the terms of a bond issue is called the indenture.

B. The unsecured long-term debts of a firm are commonly called debentures.

C. An agreement giving the bond issuer the option to repurchase the bond at a specified price prior to maturity is called the zero provision.

D. A special account that sets aside periodic payments for bond redemption is called a sinking fund.

Question 13 of 25

Which of the following statements regarding bond trading is INCORRECT?

A. The long-term bonds issued by state and local governments in the United States are called municipal bonds.

B. The long-term bonds issued by the U.S. government are called Treasury Bills.

C. A bond that makes no coupon payments (and thus is initially priced at a deep discount) is called a zero coupon bond.

D. The price a dealer is willing to pay for a security is called the bid price.

Question 14 of 25

Which bond would most likely possess the least degree of interest rate risk?

A. 8% coupon rate, 12 years to maturity

B. 8% coupon rate, 15 years to maturity

C. 10% coupon rate, 10 years to maturity

D. 12% coupon rate, 8 years to maturity

Question 15 of 25

What is the value of a bond that will pay a total of 50 semiannual coupons of $80 each over the remainder of its life? The yield to maturity is 12%, p.a. Note: B = C [{1 â 1/(1+y)t}/y] + F /(1+y)t. Be careful about specifying t and y for this semiannual bond.

A. $ 734.86

B. $ 942.26

C. $1,135.90

D. $1,315.24

Question 16 of 25

Dizzy Corporationâs 10-year semiannual bond bearing a coupon rate of 12% is currently selling for $950. Given this information, which of the following is the correct valuation equation for this bond?

A. B = 120 [PVIFA(12%, 10)] + 1,000 [PVIF(12%, 10)]

B. $950 = 60 [PVIFA(r/2, 20)] + 1,000 [PVIF(r/2, 20)]

C. $950 = 120 [PVIFA(r, 10)] + 1,000 [PVIF(r, 10)]

D. B = 60 [PVIFA(6%, 20)] + 1,000 [PVIF(6%, 20)]

Question 17 of 25

To find the yield-to-maturity of the bond in Question #16 by trial and error, which number (as a semiannual YTM) should you pick as your first try?

A. 5%

B. 6%

C. 7%

D. Any number (like one of your favorite lotto numbers).

Question 18 of 25

George bought an investment one year ago and just calculated his return on investment. He found that his purchasing power has increased by 15% as a result of his investment. If the inflation over the period was 4%, his _______________. Note: (1+R) = (1+r)(1+h), but you donât need calculation here.

A. real return on investment is more than 15%

B. nominal return on investment is more than 15%

C. nominal return on investment is 11%

D. real return on investment is equal to 4%

Question 19 of 25

Which statement is INCORRECT given the following Treasury quotes? Maturity Coupon Bid Ask(ed) Chg Ask(ed) Yld ---------------------------------------------------------------------------------------- 5/15/2030 6.250 150.7188 150.7500 .8906 2.713

A. The amount of each coupon on this bond is $31.25.

B. The ask(ed) price is $1,507.50.

C. The dealer is willing to sell this bond to you for 150.7188% of par.

D. This bondâs ask(ed) price rose by $8.906 (i.e., eight dollars and 90+ cents) from the previous trading day.

Question 20 of 25

Which of the following statements regarding stock trading is INCORRECT?

A. Stock that has priority for dividends and bankruptcy liquidation is called priority equity.

B. The short alphabetic abbreviation for an exchange-listed stock by which the issue is identified in the market is called the stock's ticker symbol.

C. Capital gains yield is the rate of return based on the stock price increase.

D. Proxy voting is the voting procedure where shareholders grant authority to another individual to vote their shares.

Question 21 of 25

What would you pay for a share of ABC Corporation stock today if the next dividend will be $3 per share, your required return on equity investments is 15%, and the stock is expected to be worth $90 one year from now? (Remember the stock price today is the PV of its future cash flows, i.e., dividends and the future stock price, properly discounted)

A. $75.00

B. $78.26

C. $80.87

D. $90.00

Question 22 of 25

A preferred stock that pays a constant dividend of $1.50 currently sells for $10.71. What is the required rate of return? Note: P0 = D/R for a preferred stock.

A. 14%

B. 13%

C. 12%

D. 10%

Question 23 of 25

A stock with a constant dividend growth rate of 5% is expected to make a $2 dividend in one year. If you require a 12% return on your investment, which of the following statements is INCORRECT? Note: P0 = D1/(Râg) or R = (D1/P0) + g.

A. The current stock price is $28.57.

B. The dividend yield is 7%.

C. The capital gains yield is 12%.

D. The stock price will grow at an annual 5%.

Question 24 of 25

McIver, Inc. currently pays a $2 annual dividend. Investors believe that dividends will grow at 20% next year, 12% for the following year, and 6% annually thereafter. The required return is 10%. What is the current price of the stock?

A. $63.27

B. $60.80

C. $58.71

D. $54.90

Question 25 of 25

Which statement is INCORRECT given the following stock quotes? Prev Close 44.34 Dayâs Range 43.45 â 44.37 Bid 44.01 x 1,200 Volume 908,587 Ask 44.02 x 400 P/E 17.26 Beta 2.4 EPS 2.55 Market Cap 10.11B Div & Yield 0.50 (1.10%)

A. At this point someone was willing to buy 1,200 shares of this stock for $44.01 a share.

B. The yield-to-maturity for this stock is 1.1%.

C. On this trading day so far 908,587 shares changed hands.

D. The total value of this companyâs stock is (about) $10,110 million.

You have $49,061.69 in a brokerage account, and you plan todeposit an additional $5,000 at the end of every future year untilyour account totals $200,000. You expect to earn 9.1% annually onthe account. How many years will it take to reach your goal? Roundyour answer to the nearest whole number.

Present and Future Value of an Uneven Cash Flow Stream

An investment will pay $100 at the end of each of the next 3years, $300 at the end of Year 4, $600 at the end of Year 5, and$800 at the end of Year 6. If other investments of equal risk earn11% annually, what is its present value? Round your answer to thenearest cent.
$

What is its future value? Round your answer to the nearestcent.
$

You want to buy a car, and a local bank will lend you $20,000.The loan would be fully amortized over 3 years (36 months), and thenominal interest rate would be 12%, with interest paid monthly.What is the monthly loan payment? Round your answer to the nearestcent.
$

What is the loan's EFF%? Round your answer to two decimalplaces.
%

Find the present values of the following cash flow streams. Theappropriate interest rate is 5%. Round your answers to the nearestcent. (Hint: It is fairly easy to work this problemdealing with the individual cash flows. However, if you have afinancial calculator, read the section of the manual that describeshow to enter cash flows such as the ones in this problem. This willtake a little time, but the investment will pay huge dividendsthroughout the course. Note that, when working with thecalculator's cash flow register, you must enter CF₀ = 0.Note also that it is quite easy to work the problem with Excel,using procedures described in the Chapter 4 Tool Kit.)

Year Cash Stream A Cash Stream B

1 $100 $300

2 400 400

3 400 400

4 400 400

5 300 100

Stream A $
Stream B $
What is the value of each cash flow stream at a 0% interestrate? Round your answers to the nearest cent.
Stream A $
Stream B $

Find the future values of the following ordinary annuities:

FV of $200 paid each 6 months for 4 years at a nominal rate of12%, compounded semiannually. Round your answer to the nearestcent.
$
FV of $100 paid each 3 months for 4 years at a nominal rate of12%, compounded quarterly. Round your answer to the nearestcent.
$
The annuities described in parts a and b have the same amountof money paid into them during the 4-year period and both earninterest at the same nominal rate, yet the annuity in part b earnsmore than the one in part a over the 4 years. Why does thisoccur?
-Select-The nominal deposits into the annuity in part (b) aregreater than the nominal deposits into the annuity in part (a). Theannuity in part (a) is compounded less frequently; therefore, moreinterest is earned on interest. The annuity in part (a) iscompounded more frequently; therefore, more interest is earned oninterest. The annuity in part (b) is compounded less frequently;therefore, more interest is earned on interest. The annuity in part(b) is compounded more frequently; therefore, more interest isearned on interest.

To complete your last year in business school and then gothrough law school, you will need $25,000 per year for 4 years,starting next year (that is, you will need to withdraw the first$25,000 one year from today). Your uncle offers to put you throughschool, and he will deposit in a bank paying 9.57% interest a sumof money that is sufficient to provide the 4 payments of $25,000each. His deposit will be made today.

How large must the deposit be? Round your answer to the nearestcent.
$
How much will be in the account immediately after you make thefirst withdrawal? Round your answer to the nearest cent.
$

How much will be in the account immediately after you make the lastwithdrawal? Round your answer to the nearest cent. Enter "0" ifrequired
$

You need to accumulate $10,000. To do so, you plan to makedeposits of $1,450 per year - with the first payment being made ayear from today - into a bank account that pays 10.24% annualinterest. Your last deposit will be less than $1,450 if less isneeded to round out to $10,000. How many years will it take you toreach your $10,000 goal? Round your answer up to the nearest wholenumber.
year(s)

How large will the last deposit be? Round your answer to thenearest cent.
$

It is now January 1. You plan to make a total of 5 deposits of$300 each, one every 6 months, with the first payment being madetoday. The bank pays a nominal interest rate of 10% butuses semiannual compounding. You plan to leave the moneyin the bank for 10 years. How much will be in your account after 10years? Round your answer to the nearest cent.
$
You must make a payment of $1,788.84 in 10 years. To get themoney for this payment, you will make 5 equal deposits, beginningtoday and for the following 4 quarters, in a bank that pays anominal interest rate of 8% with quarterly compounding.How large must each of the 5 payments be? Round your answer to thenearest cent.
$

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CISC 121 Lecture Notes - Lecture 10: Life Annuity, Life Insurance, Random Variable

CISC 121 Full Course Notes

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Related Questions

Year	Cash Stream A	Cash Stream B
1	$100	$300
2	400	400
3	400	400
4	400	400
5	300	100