Question

____​10.​Which of the following statements is NOT CORRECT?

a.

The present value of a 3-year, $150 annuity due will exceed the present value of a 3-year, $150 ordinary annuity.

b.

If a loan has a nominal annual rate of 8%, then the effective rate can never be less than 8%.

c.

If a loan or investment has annual payments, then the effective, periodic, and nominal rates of interest will all be the same.

d.

The proportion of the payment that goes toward interest on a fully amortized loan declines over time.

e.

An investment that has a nominal rate of 6% with semiannual payments will have an effective rate that is less than 6%.

____​11.​Last year Toto Corporation's sales were $225 million. If sales grow at 6% per year, how large (in millions) will they be 5 years later?

a.

$271.74

b.

$286.05

c.

$301.10

d.

$316.16

e.

$331.96

____​12.​You deposit $1,000 today in a savings account that pays 3.5% interest, compounded annually. How much will your account be worth at the end of 25 years?

a.

$2,245.08

b.

$2,363.24

c.

$2,481.41

d.

$2,605.48

e.

$2,735.75

____​13.​Suppose a U.S. government bond promises to pay $1,000 five years from now. If the going interest rate on 5-year government bonds is 5.5%, how much is the bond worth today?

a.

$765.13

b.

$803.39

c.

$843.56

d.

$885.74

e.

$930.03

____​14.​How much would $5,000 due in 50 years be worth today if the discount rate were 7.5%?

a.

$109.51

b.

$115.27

c.

$121.34

d.

$127.72

e.

$134.45

____​15.​Suppose the U.S. Treasury offers to sell you a bond for $747.25. No payments will be made until the bond matures 5 years from now, at which time it will be redeemed for $1,000. What interest rate would you earn if you bought this bond at the offer price?

a.

4.37%

b.

4.86%

c.

5.40%

d.

6.00%

e.

6.60%

____​16.​Ten years ago, Levin Inc. earned $0.50 per share. Its earnings this year were $2.20. What was the growth rate in Levin's earnings per share (EPS) over the 10-year period?

a.

15.17%

b.

15.97%

c.

16.77%

d.

17.61%

e.

18.49%

____​17.​How many years would it take $50 to triple if it were invested in a bank that pays 3.8% per year?

a.

23.99

b.

25.26

c.

26.58

d.

27.98

e.

29.46

____​18.​You want to buy a new sports car 3 years from now, and you plan to save $4,200 per year, beginning one year from today. You will deposit your savings in an account that pays 5.2% interest. How much will you have just after you make the 3rd deposit, 3 years from now?

a.

$11,973.07

b.

$12,603.23

c.

$13,266.56

d.

$13,929.88

e.

$14,626.38

____​19.​You want to buy a new sports car 3 years from now, and you plan to save $4,200 per year, beginning immediately. You will make 3 deposits in an account that pays 5.2% interest. Under these assumptions, how much will you have 3 years from today?

a.

$13,956.42

b.

$14,654.24

c.

$15,386.95

d.

$16,156.30

e.

$16,964.11

Answer 1

a.The present value of a 3-year, $150 annuity due will exceed the present value of a 3-year, $150 ordinary annuity.

Ans: Yes

Annuity due is an annuity whose payment is due immediately at the beginning of each period.Annuity due can be contrasted with an ordinary annuity where payments are made at the end of each period.

PV Annuity​ Due=C*[(1+i)^-n-1/i]*1+i

If we plug the same numbers as above into the equation, here is the result:(take 5% as interest rate)

PV Annuity Due​​=$1,50*[1-(1+0.05)^-3/0.05]*1+0.05

=150*[1-1.16/0.05]*1.05

=150*-0.15*1.05=$504

PVOrdinary Annuity=C*[(1+i)^-n-1/i]

=150*[1-1.16/0.05]

=150*-3.2=$480

If we plug the same numbers as above into the equation, here is the result:(take 5% as interest rate)

b.If a loan has a nominal annual rate of 8%, then the effective rate can never be less than 8%.

Ans:Yes

An interest rate takes two forms: nominal interest rate and effective interest rate. The nominal interest rate does not take into account the compounding period. The effective interest rate does take the compounding period into account and thus is a more accurate measure of interest charges.

A statement that the "interest rate is 8%" means that interest is 8% per year, compounded annually. In this case, the nominal annual interest rate is 8%, and the effective annual interest rate is also 8%. However, if compounding is more frequent than once per year, then the effective interest rate will be greater than 8%. The more often compounding occurs, the higher the effective interest rate.

The relationship between nominal annual and effective annual interest rates is:

i_a = [ 1 + (r / m) ] ^m - 1

where "i_a" is the effective annual interest rate, "r" is the nominal annual interest rate, and "m" is the number of compounding periods per year.

c.If a loan or investment has annual payments, then the effective, periodic, and nominal rates of interest will all be the same.

Ans: No

The effective annual interest rate is the real return on a savings account or any interest-paying investment when the effects of compounding over time are taken into account.

A periodic interest rate is a rate that can be charged on a loan, or realized on an investment over a specific period of time.

Nominal interest rate refers to the interest rate before taking inflation into account.

d.The proportion of the payment that goes toward interest on a fully amortized loan declines over time.

Ans: Yes

An amortized loan is a type of loan with scheduled, periodic payments that are applied to both the loan's principal amount and the interest accrued. An amortized loan payment first pays off the relevant interest expense for the period, after which the remainder of the payment is put toward reducing the principal amount. Common amortized loans include auto loans, home loans, and personal loans from a bank for small projects etc.

As the interest portion of the payments for an amortization loan decreases, the principal portion increases.

e.An investment that has a nominal rate of 6% with semiannual payments will have an effective rate that is less than 6%. Ans:No

a,b and d are correct statements

11.Last year Toto Corporation's sales were $225 million. If sales grow at 6% per year, how large (in millions) will they be 5 years later?

Ans:$301,1 million

Use the formula for compound interest/growth:

A=P(1+r)ⁿ r =represents the rate as a decimal)

=225*1.06⁵ (working in millions) n = the number of years.

=301.10

12.You deposit $1,000 today in a savings account that pays 3.5% interest, compounded annually. How much will your account be worth at the end of 25 years?

Ans:$2363.24

FV=P[1+r/n]^nt

=$1000[1+0.035/1]^1*25

=$1000*1.035²⁵

=$2363.24

13.Suppose a U.S. government bond promises to pay $1,000 five years from now. If the going interest rate on 5-year government bonds is 5.5%, how much is the bond worth today?

Ans:$765.13

PV=$1000/(1+0.055)⁵

  =$1000/1.30696

=$765.13

14.How much would $5,000 due in 50 years be worth today if the discount rate were 7.5%?

Ans:134.45

Present Value=FV/(1+r)ⁿ

⁼5000/1+0.075)⁵⁰

⁼134.45

15.Suppose the U.S. Treasury offers to sell you a bond for $747.25. No payments will be made until the bond matures 5 years from now, at which time it will be redeemed for $1,000. What interest rate would you earn if you bought this bond at the offer price?

Ans:6.00%

16.Ten years ago, Levin Inc. earned $0.50 per share. Its earnings this year were $2.20. What was the growth rate in Levin's earnings per share (EPS) over the 10-year period?

Ans:15.97%

(End value/Begining value)^1/t -1 *100

(2.20/0.50)^1/10 -1 *100=15.97

{2.20/0.50=4.4

=(4.4)^1/10 =1.597

=1.597-1

=0.1597

=0.1597*100

=15.97}

17.How many years would it take $50 to triple if it were invested in a bank that pays 3.8% per year?

Ans:29.45

Assuming it's compound interest, and the interest is paid annually (you should specify that):
150 = 50*(1 + 0.038)^n
1.038^n = 3

n*log(1.038) = log(3)
n = log(3)/log(1.038)
n =~ 29.4567 years

18.You want to buy a new sports car 3 years from now, and you plan to save $4,200 per year, beginning one year from today. You will deposit your savings in an account that pays 5.2% interest. How much will you have just after you make the 3rd deposit, 3 years from now?

Ans:$13289.86

Year	Year Interest	Total Interest	Balance
1	$218.40	$218.40	$4,418.40
2	$229.76	$448.16	$4,648.16
3	$241.70	$689.86	$4,889.86

4200*3=12600+689.86=13289.86