FNAN 303 Lecture Notes - Lecture 4: Cash Flow, Sign Convention

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gmubusstudent

15 Mar 2021

School

George Mason University

Department

Finance

Course

FNAN 303

Professor

Ben Drissi Messouak

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Document Summary

Time value of money (tvm) 3 slides 1-38. The future value at a given point in time of multiple cash flows that occur at different points in time is the sum of the future values of each individual cash flow. = [c0 (1 + r)t] + [c1 (1 + r)t-1] + [c2 (1 + r)t-2] + + [ck (1 + r)t-k] + . + [ct-1 (1 + r)1] + [ct] ,000 in her account in 9 years: solution, fv9 = [c0 x (1 + r)9] + [c4 x (1 + r)9-4, so, 20,000 = [5,000 x (1. 120)9] + [c4 x 1. 1205] = 13,865 + [c4 x 1. 1205: so, 20,000 13,865 = [c4 1. 1205] = 6,135, so, c4 = [6,135 / 1. 1205] = ,481. Fvt = fv(c1) + fv(c2) + + fv(ct) = [c (1+r)t-1] + [c (1+r)t-2] + + [c]

Related Questions

Problem 1:

Paltrow Company made an investment in another that guarantees cash flow $ 22,500 each year for the next five years. If the company uses a discount rate of 15% on their investments, what is the present value of this investment?

Problem 2:

The company Argentinian Grill has a 7-year loan $ 23.500 with the local bank. His plan is to start paying the loan in seven equal installments starting today. If the interest rate
It is 8.4%, calculates the annuity payment.

Problem 3:

You currently have 25 and want to retire at the age of 65. As a complement to other sources of retirement, you could deposit $ 3,000 at the end of each year in an IRA. This financial instrument would earn 9.75% over the next 40 years.

a) How much money will accumulate at the end when you turn 65?

Problem 4:
Solve each situation separately, where P = principal; r = interest rate; t = time in years; I = interest and future value FV =

A) P = $ 10.800; r = 6.50%; t = 7 years; I =?

B) I = $ 1.550; t = 11 months r = 7.75%; P =?

C) P = $ 30.500; r = 6.75%; t = 10; VF =

D) FV = $ 320,000; r = 5.40% compounded monthly; t = 30; P =?

b) If you decide to wait 10 years to begin to deposit, how much money will accumulate to reach age 65?

c) Discuss the impact of waiting 10 years on the accumulated amount.

Problem 5:

You want to start a bakery business. For this, you will need a capital of $ 75,000 to start operating. If you have to operate within four years. What sum must now invest 12% quarterly composite, the amount needed to keep and operate your business?

** NOTE** IT IS VERY IMPORTANT TO COMPLETE THE ENTIRE EXERSICE. INCLUDE ALL THE CALCULATIONS, PLEASE, THANK

pinkhorse326

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

Assume that you have $1,000 to invest, so insert 1000 as your Present Value in the following table. Assume that you want to invest your money for 5 years (insert 5 for Number of Periods). Assume an annual interest rate of 3.00% (insert 3 for Interest Rate per Period). The table will determine the Future Value of your investment. If you input the numbers correctly, your Future Value is computed to be $1.159, which is what your investment will be worth in 5 years. Now revise the input to reflect your actual savings and the prevailing interest rate so that you can see how your savings will grow in 5 years. Even if you have no savings now, you can at least see how the interest rate affects the future value of savings by revising your input in the Interest Rate per Period and then observing the change in the Future Value. Future Value of a Present Amount Present Value $1,500 Number of Periods 5 Interest Rate per Period 3.0% FV = PV*(1+R)^N Future Value $1,739 2. Assume that you have $1,000 to invest at the end of each of the next 5 years, so insert 1000 as your Payment per Period in the following table. Assume that you want to invest your money for 5 years (insert 5 for Number of Periods). Assume an annual interest rate of 3.00% (insert 3 for Interest Rate per Period). The following table will determine the Future Value of your investment. If you input the numbers correctly, your Future Value is computed to be $5,309, which is what your investments will be worth in 5 years. Now revise the input to reflect your actual expected savings per year over the next 5 years, and existing interest rate quotations so that you can estimate how your savings will grow in 5 years. You can now revise the table to fit your own desired level of saving. Future Value of an Annuity Payment per Period $1,500 Number of Periods 5 Interest Rate per Period 3.0% FV = FV(R, N, PMT, (PV), beginning=1, end=0) Future Value $7,964 3. Assume that you want to deposit savings that will be worth $10,000 in 5 years, so insert 10000 as the Future Amount and 5 as the Number of Periods in the following table. Assume an annual interest rate of 3.00% (insert 3 for Interest Rate per Period). The following table will determine the Present Value, which represents the amount of savings you need today that would accumulate to be worth $10,000 in 5 years. If you input the numbers correctly, the Present Value is estimated in the table to be $8,606. Now revise the input to reflect your own desired savings amount in 5 years so that you can estimate how much you need now to achieve your savings goal in 5 years. Present Value of a Future Amount Future Amount $20,000 Number of Periods 5 Interest Rate per Period 3.0% PV = FV / (1+R)^N Present Value $17,252 4. Assume that you want to deposit savings at the end of each of the next 5 years so that you will have $10,000 in 5 years. So insert 10000 as the Future Amount and 5 for Number of Periods. Assume an annual interest rate of 3.00% (insert 3 for Interest Rate per Period). The following table will determine the Annual Payment, which represents the annual payments that will accumulate to your future desired investment. If you input the numbers correctly, your Annual Payment is computed to be $1,884. Now revise the input to reflect your own desired savings amount in 5 years so that you can estimate how much you need to save per year to achieve your savings goal in 5 years. Compute Payment Needed to Achieve Future Amount Future Amount $20,000.00 Number of Periods 5.00 Interest Rate per Period 3.00% PMT = FV / [FV(R, N, -1)] Annual Payment $3,767

Decisions 1. Using the above formulas and understanding of the impact of interest rates and time on your savings, report on how much you must save per year and the return you must earn to meet your savings goal for graduation, and your savings goal in your first three years of post-graduation life.

I need a report on how much to save per year and the return to earn to meet savings goal for graduation, and savings goal in the first three years of post graduation. Can you please use the numbers above that are already calculated in the formula. I have had an answer on this below. I don't understand why the periods don't stay the same for 5 years. The annuity is 7964 I took that divided b y 60 = 132.7 per month and multiplied it by 12 for a year and got 1592.4. Is that the savings for the answer to saving for a year. IF not I need help figuring out the calculation for the return to meet after gradutaion and the next three years post graduation.

Goal 1	Savings Goal for graduation, FV	$ 20,000

	Time till graduation (Number of periods)	5

	Present value of savings	$ -

	Expected interest rates	3%

	Savings needed per year, PMT	$3,767.09	=PMT(3%,5,0,20000,)

Goal 2	Savings Goal for 1st year of post graduation, FV	$ 15,000

	Time till post graduation year 1 (Number of periods)	6

	Present value of savings	$ -

	Expected interest rates	3%

	Savings needed per year, PMT	$2,318.96	=PMT(3%,6,0,15000,)

Goal 3	Savings Goal for 2nd year of post graduation, FV	$ 15,300

	Time till post graduation year 1 (Number of periods)	7

	Present value of savings	$ -

	Expected interest rates	3%

	Savings needed per year, PMT	$1,996.75	=PMT(3%,7,0,15300,)

Goal 4	Savings Goal for 3rd year of post graduation, FV	$ 15,606

	Time till post graduation year 1 (Number of periods)	8

	Present value of savings	$ -

	Expected interest rates	3%

	Savings needed per year, PMT	$1,754.99	=PMT(3%,8,0,15606,)

FNAN 303 Lecture Notes - Lecture 4: Cash Flow, Sign Convention

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