๐Ÿท๏ธ LIMITED TIME OFFER: GET 20% OFF GRADE+ YEARLY SUBSCRIPTION โ†’
Log in
Finance
1
answer
0
watching
175
views

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 6th year

d.

present value of a perpetuity of $50, with the first paymentreceived at the end of the 16th 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 = 50*4.3295 = $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 = 50*6.7101 = $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.

Watch
1
answer
0
watching
175
views

For unlimited access to Homework Help, a Homework+ subscription is required.

Tod Thiel
Tod ThielLv2
30 Sep 2019

Unlock all answers

Get 1 free homework help answer.
Already have an account? Log in
Share

Related questions

4.3

NOTE: Please show all calculations (no Excel solutions please)to four decimal places if applicable: Calculate the followingvalues, assuming a discount rate of 8%:

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 6th year

d.

present value of a perpetuity of $50, with the first paymentreceived at the end of the 16th year.

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 รขย€ย“ 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

What is the relationship between discounting and compounding?

What is the relationship between the present-value factor and the annuity present-value factor?

What will $5,000 invested for 10 years at 8 percent compounded annually grow to? How many years will it take $400 to grow to $1,671 if it is invested at 10 percent compounded annually? At what rate would $1,000 have to be invested to grow to $4,046 in 10 years?

Calculate the future sum of $1,000, given that it will be held in the bank for 5 years and earn 10 percent compounded semiannually.

What is an annuity due? How does this differ from an ordinary annuity?

What is the present value of an ordinary annuity of $1,000 per year for 7 years discounted back to the present at 10 percent? What would be the present value if it were an annuity due?

What is the future value of an ordinary annuity of $1,000 per year for 7 years compounded at 10%? What would be the future value if it were an annuity due?

You have just borrowed $100,000, and you agree to pay it back over the next 25 years in 25 equal end-of-year payments plus 10 percent compound interest on the unpaid balance. What will be the size of these payments?

What is the present value of a $1,000 perpetuity discounted back to the present at 8 percent?

What is the present value of a $1,000 annuity for 10 years, with the first payment occurring at the end of year 10 (that is, ten $1,000 payments occurring at the end of year 10 through 19), given a discount rate of 10 percent?

Given a 10 percent discount rate, what is the present value of an perpetuity of $1,000 per year if the first payment does not begin until the end of year 10?

Weekly leaderboard

Home
Homework Help 3,900,000
Finance 370,000
Start filling in the gaps now
Log in