FIN 300 Lecture Notes - Lecture 5: Nominal Interest Rate, Yield Curve, Real Interest Rate

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14 Oct 2017

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Effective annual rate: this rate is compounded once per year. It represents the true rate of interest that a lender earns (and a borrower pays) each year. If there are m payment periods per year, the interest rate per payment period is given by (1. If payment periods are monthly, a quoted ear of 6% converts to an interest rate per month of r = (1. 06) Annual percentage rate: this rate is compounded once per year payment period, by law, the apr must be disclosed for all non-mortgage loans. If there are m payment periods per year, the interest rate per payment period is given by r = apr / If payment periods are monthly, a quoted 6% apr converts to an interest rate per month of. Mortgage rate: this rate is compounded twice per year, by law, this rate must be quoted on all mortgages.

Related Questions

CAN SOMEONE LET ME KNOW IF I DID THESE RIGHT?? PLEASE

1. What is the effective rate of interest for an investment paying 18% compounded monthly?

Effective rate of interest= (1+r)^n-1

r= 18% or .18; compounded monthly= 0.18/12

N= no of period ie 12

Effective rate r= (1+.18/12)^12-1

= 0.1956 ie 19.56%

2. If you want to buy a $25,000 car in 5 years, what single amount must you invest now at 10% compounded quarterly to have the money to pay cash?

Fv= PV(1+i)^n

Fv= 25,000 n=5 years so 5*4= 20 periods; r = 10% compounded quarterly ie .10/4

25,000=PV(1+.10/4)^20

25,000= PV (4.10/4)^20

PV= (25,000/1.025)^20

PV=$15,256.77

3. What is the present value of $50,000, 4 years from now at 12% interest compounded monthly?

Fv= Pv (1+r)^n

Fv=50,000; Pv?; n= 4 years compounded monthly ie 48; R= 12% compounded monthly ie .12/12

50,000= PV (1+.12/12)^48

PV=50,000/(1.01)^48

PV=$31,013.02

4. What is the future value of $5,000 in 15 years if you can earn 12% interest compounded semi-annually?

Fv=PV(1+i)^n

Fv=5,000; n=15 years semi annually= 30 periods; I=12% compounded semi annually=.12/2

5,000= PV (1+.12/2)^30

PV=5,000(1.06)^30

PV=$28,717.46

5. What is the future value of $800 deposited annually at 9% interest for 25 years if the deposits are made at the end of the period? And, if the deposits are made at the beginning of the period?

FV(end)= PMT[(1+i)^n-1)/i] (Ordinary annuity)

FV= $800; i=9% or .09; n=25 years

Fv+800[(1+0.09)^25-1)/0.09

FV=$67,760.72

FV=(beginning)= PMT[((1+i)^n-1)/i](1+r)

FV=$800; I=9% or 0.09; n=25 years

FV=800[(1+0.09)^25-1)/0.09)(1+0.09)

FV=$73,859.18

6. Using the information from the previous problem, how much more interest is earned from the annuity due than from the ordinary annuity?

Annuity due= annuity (beginning) - ordinary annuity

=$73,859.18-$67,760.72= $6,098.46

7. How much must be deposited now in order to withdraw $15,000 at the end of each year for 30 years, if interest is 11% compounded annually?

Annuity the end of each year= 15,000

N=30 years; r= 11% compounded annually

To find PV of an annuity of $15,000 @ the end of each of the year

PV= PMT [1-(I+i)^-n/i

PV=15,000[1-(I+0.11)^-30/0.11]

PV= PMT[1-(I+i)^-n/i

=$130,406.89

8. If you want $2,000,000 in your retirement fund in 45 years, and you can earn 14% compounded annually, what will be your annual contribution? How much interest will you earn?

FV= 2,000,000; N= 45 years; i= 14% compounded annually

We have the FV of an annuity â to find the annuity

FV= PMT [(I+i)^n-1)/i]

2,000,000=PMT [((1+0.14)^45-1)/(0.14]

2,000,000= PMT [2590.5648]

PMT=$772.03

9. If you retire with $1,375,000 in your retirement fund and plan to live for 20 years, how much can you withdraw every year if your investment earns 10%?

PV= 1,375,000 n=20 years i=10%

To find annuity given the PV

PV=PMT [1-(1+i)^-n/I]

1,375,000= PMT [1-(1+0.10)^-20/0.10)

PMT(yearly withdrawl) =$161,506.98

10. How much more interest is earned from ordinary annuity payments of $6,000 per year for 25 years if you can increase your rate of interest from 6% to 9%?

PMT=$6,000 per year; n=25 years; i=6% to 9%

Interest at 6%

FV= PMT [((1+r)^25-1)/0.06]

FV= 6,000[((1+0.06)^25-1)/0.06]

=$329,187.07

Interest at 9%

FV=6,000[(91+0.09)25-1)/0.09]

= $508,205.38

More earned interest 9%- 6% = $508,209.38 - $329,187.07 = $179,018.31

sapphiresnake702

Use a calculator to solve all quantitative problems, and be sure to show calculator format!!!

(n, I, pmt, pv, fv CFo,I,CF1, CF2â¦.)

8) Three years ago a company had sales of $300,000. Now sales are $1,000,000. At what rate have

sales been growing?

9) Define each of the following:

a) Quoted rate (APR)

b) Periodic rate

c) Effective annual rate (EAR)

10) What are the following Effective Annual Rates (EAR) for 12%:

a) Compounded semiannually?

b) Compounded quarterly?

c) Compounded daily?

11) What would the value of $500 be after 4 years, assuming a return of 8% per year:

a) with semiannual compounding?

b) with quarterly compounding?

12)A. You plan to invest in a preferred stock issue that pays a $60 dividend at the end of each year. Based

on market conditions, you want to get a 5% return. What are you willing to pay for this security?

12)A You want to buy a car today!! The used car you are looking at costs $21,500. The car dealer will

charge you 5% interest on the three year car loan you need. You will be borrowing the whole $21,500. What will your car payment be, if you will make monthly payments?

13. Your company has invested $2500 in a vending machine today. You expect the machine to last 10 years and to produce the following after tax cash flows per year:

Year 1 $100

Year2 $250

Year 3 $250

Year 4 $300

Year 5 $300

Year 6 $300

Year 7 $300

Year 8 $300

Year 9 $350

Year 10 $350

If you have a required return on your investment of 7%, did you pay too much for the vending machine?

please show me calculation/workings

try to solve as many as possible please

5. Your friend is considering investing $5,000 at the end of every quarter in a bank account

paying 8% per annum. The first contribution will be made at the end of the first quarter. If

interest is compounded monthly, the total amount she will have accumulated at the end of ten

years is closest to:

a) $228,338.

b) $289,731.

c) $302,010.

d) $302,886.

6. Banks A, B and C offer the following interest rates on one-year bank deposits.

Bank A: 7.9% p.a. compounded monthly.

Bank B: 8.0% p.a. compounded quarterly.

Bank C: 8.1% p.a. compounded semi-annually.

The best interest rate is offered by:

a) Bank A.

b) Bank B.

c) Bank C.

d) The three banks offer equally attractive interest rates.

7. You are thinking about buying a rare collectible that costs $50,000. The dealer is proposing

the following deal. She will lend you the money and you will repay the loan by making the

same payment every two years for the next 20 years. If the interest rate is 4% p.a.

compounded annually, the amount you will have to pay every two years is closest to:

a) $3,679.

b) $5,153.

c) $6,165.

d) $7,505.

8. BLB Ltd has just issued a âcoupon growth bondâ with the following terms. Each bondâs face

value is $1,000 and the bonds will mature in 5 yearsâ time. Coupons will be paid on an annual

basis at the end of each year. The first yearâs coupon will be $100 which will then grow at an

annual rate of 10% until the bonds mature. If the bondâs yield to maturity is 8% per annum, its

price today should be closest to:

a) $972.

b) $1,080.

c) $1,161.

d) $1,275.

9. Consider a five-year bond with a face value of $1,000 paying annual coupons at a rate of 12%

which has a current yield to maturity of 10%. If all interest rates remain unchanged, one year

from today the price of this bond:

a) Will be higher.

b) Will be lower.

c) Will be the same.

d) Cannot be determined without additional information.

10. Your favorite aunty has finally agreed to contribute towards funding your retirement.

Specifically, she will start with a contribution of $6,000 today (that is, end of year 0) but this

amount will then decline at a constant rate of 3% p.a. over the foreseeable future. If the

interest rate appropriate for valuing your auntyâs contribution is 12% p.a. its present value

today is closest to:

a) $38,800.

b) $44,800.

c) $56,000.

d) $70,667.

11. The earnings and dividends of XYX Ltd are expected to grow at a rate of 5%, 10% and 15%

p.a. during years 1 through 3 respectively. After that, the earnings and dividends are expected

to stabilize to a long-run growth rate of 5% p.a. forever. The companyâs current dividend per

share is $1.50 and the required rate of return on the stock is 12% p.a. Based on this

information, the current price should be closest to:

a) $21.27.

b) $25.48.

c) $28.07.

d) $29.89.

12. DBD Ltdâs current dividend and price per share are $1.80 and $10.00 respectively. Market

analysts expect the dividend per share to grow at a constant annual rate over the foreseeable

future. If the expected return on this stock is 15% per annum, the constant annual growth rate

implied by this information is closest to:

a) â3.0%.

b) â2.5%.

c) 2.5%.

d) 3.0%.

13. Market analysts expect the earnings per share of JJC Ltd to be $3.00 next year. The company

has typically retained 60% of its earnings and this policy is expected to continue in the

foreseeable future. The return required by investors on companies in JJCâs risk class is 10%

p.a. If the companyâs earnings and dividends are expected to grow at a constant rate of 4%

p.a., the current share price is closest to:

a) $20.00.

b) $20.80.

c) $30.00.

d) $31.80.

14. You have just settled a lawsuit in your favor and you will be receiving semi-annual payments

of $25,000 over the next ten years. The first payment will occur six months from today. You

plan on investing these payments and you expect to earn a return of 6% p.a. with the returns

compounded monthly. The present value of this investment is closest to:

a) $329,520.

b) $368,004.

c) $370,642.

d) $371,937.

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FIN 300 Lecture Notes - Lecture 5: Nominal Interest Rate, Yield Curve, Real Interest Rate

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