BFN 110 Lecture Notes - Lecture 4: Tunxis Community College

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coralimpala133

6 Jan 2021

School

Tunxis Community College

Department

Business – Finance

Course

BFN 110

Professor

garside

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Document Summary

Annuities are a special case of multiple cash flows. An annuity is a no. of equal cash flows occurring at equal time intervals. An ordinary annuity assumes all cash flows occur at the end of each period. Both the fv and pv of an annuity can be calculated using the previous formulas. Rose deposits k into a bank account at the end of each year for the next 3 years. Deposit every 3 months into a back account for next 7 years, interest rate is 6% p. a. compounded quarterly. The pv of an ordinary annuity is calculated at the beginning of the period. Ordinary annuities have payments occurring at the end of each period. Pv = 20,000 [1- (1. 005)-240 / 0. 005] = ,791,615. 43. Pv = ,000, 15 years, 6% monthly . You get 500k initially and then 50k every year for 10 years.

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

4.3	Need help with 4.4 a and b at bottom. 4.3 is required to answerthis. Calculate the following values, assuming a discount rate of8%:
	a.	present value of a perpetuity (also called a perpetual annuity)of $50 received each year at the end of each year
	b.	present value of an annuity of $50 received at the end of eachyear for 5 years
	c.	present value of an annuity of $50 received at the end of eachyear for 10 years, with the first payment to be received at the endof the 6^th year
	d.	present value of a perpetuity of $50, with the first paymentreceived at the end of the 16^th year. *ANSWER:* a. PV of perpetuity = A/i where A is annual payment &i is disc rate SO PV of Perpetuity = 50/8% = $625.00 b. Here it is PV of annuity for n=5 & PMT=$50 SO PVA = PMT(PVIFAi,n) i.e. PVA = $50(PVIFA8%,5). From PV of annuity Table, we get (PVIFA8%,5) = 4.3295 So PVA = 504.3295 = $216.48 c. This has 2 parts. First Find the PV of Annuity at 6 yrs &then find the PV of that amount at T0. Here it is PV of annuity for n=10 & PMT=$50 SO PVA = PMT(PVIFAi,n) i.e. PVA = $50(PVIFA8%,10). From PV of annuity Table, we get (PVIFA8%,5) = 6.7101 So PVA = 506.7101 = $335.51 Now PV = FV/(1+i)^n = $335.51/(1+8%)^6 = $211.43 d. This has 2 parts. First Find the PV of Perpetuity at 16 yrs& then find the PV of that amount at T0. PV of Perpetuity = A/i = 50/8% = $625 Now PV of this amount PV = 625/(1+8%)^16 = $182.43
4.4	a.	Show (with a time line, for example) that the perpetuity in4.3a. is exactly the same as the sum of the annuities andperpetuities in 4.3b. to 4.3d.
	b.	Show that their present values add up to the same amount.

violetpig294

Number of Periods of an Annuity

You have $43,061.65 in a brokerage account, and you plan to deposit an additional $4,500 at the end of every future year until your account totals $225,000. You expect to earn 6.7% annually on the account. How many years will it take to reach your goal? Round your answer to two decimal places.

years

Present Value of an Annuity

Find the present value of the following ordinary annuities. Round your answers to the nearest cent. (Notes: If you are using a financial calculator, you can enter the known values and then press the appropriate key to find the unknown variable. Then, without clearing the TVM register, you can "override" the variable that changes by simply entering a new value for it and then pressing the key for the unknown variable to obtain the second answer. This procedure can be used in many situations, to see how changes in input variables affect the output variable. Also, note that you can leave values in the TVM register, switch to Begin Mode, press FV, and find the FV of the annuity due.)

$600 per year for 10 years at 6%.
$

$300 per year for 5 years at 3%.
$

$600 per year for 5 years at 0%.
$

Now rework parts a, b, and c assuming that payments are made at the beginning of each year; that is, they are annuities due.

$600 per year for 10 years at 6%.
$

$300 per year for 5 years at 3%.
$

$600 per year for 5 years at 0%.
$

silvertrout757

BFN 110 Lecture Notes - Lecture 4: Tunxis Community College

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