Please provide the value for each component N= , I=, PV=, FV=, etc so I can lear

Question

Please provide the value for each component N= , I=, PV=, FV=, etc so I can learn how to do it in the calculator. thank you

Annuity payment for expected Future Value
6.  You wish to retire with $5 Million in 38 years. You estimate you will earn 8% annually on your

investments. How much must you invest each year in order to reach your goal?a) Ordinary (1st payment made at the end of the year)b) Due (1st payment made today)

7.  You would like to withdraw $80,000 per year during retirement. You expect to live 20 yearsafter you retire at age 65. How much do you need to have saved by the time you retire if you can

earn 4% on your funds?

Present Value of an Annuity
8.  As part of an agreement for investing in a start-up company, you will receive $10,000 at the endof each year for the next 3 years. If the agreed upon interest rate is 15%, what is the amount of

money you are required to invest.

9.  Part A) From the sale of your family property, you will receive $25,000 today and again eachyear for the next 15 years. If the discount rate is 7%, compute the present value of your future

payments.Part B) Instead of receiving annual payments, you could receive $200,000 lump sum. Should youtake the lump sum instead?

Perpetuity
10.  You plan to purchase a small service company. You anticipate receiving annual cash flows of$60,000 per year indefinitely. (A) If you require an 8% return on your investment, what is themost you should pay for this company? (B) What is the NPV if you can purchase it for $500,000?

Explanation / Answer

Ordinary annuity

Formula for future value of Annuity :

FV= A [ (1+k)n-1/k]

FV = Future annuity value=5000000

A = periodical ( Yearly) investment=$?

K=interest rate per month =8%

n=38 years

so 5000000=A*[(1.08)^38-1]/0.08

A=$22694.68

So Annual amount to be deposited =$22,694.68

Annuity due

P = (PMT [((1 + r)n - 1) / r])*(1 + r)

Where:

P = The future value of the annuity stream to be paid in the future=5000,000

PMT = The amount of each annuity payment

r = The interest rate=8% pa

n = The number of periods over which payments are to be made=38 years

5000000=PMT[(1.08^38-1)/0.08]*1.08

PMT =21013.59

So Annual deposit for annuity due =$21,013.59

7.

Formula for future value of Annuity :

FV= A [ (1+k)n-1/k]

FV = Future annuity value=?

A = periodical ( Yearly) payment =80000

K=interest rate per month =4%

n=20 years

FV =80000*[(1.04^20-1)]/0.04

=2382246.29

So the required retirement fund value =$2,382,246.29

8.

Formula for present value of an annuity = PV= A [ (1+k)n-1/k(1+k)n]

PV = Present value of fund

A = periodical installments =yearly payment=10000

k=interest rate=15% pa

n=periods=3 yrs

PV =10000*[1.15^3-1]/0.15*1.15^3=22832.25

So amount to be invested now =$22832.25

9.

Formula for present value of an annuity due = PV= A [ (1+k)n-1/k(1+k)n]*(1+k)

PV = Present value of fund

A = periodical installments =yearly payment=25000

k=interest rate=7% pa

n=periods=15yrs

PV annuity due=25000*[(1.07^15-1)/0.07*1.07^15]*1.07=243,636.7

So present value of annuity due =$243,636.7

As the PV is more than $200,000 offered as lump sum, I should not accept lump sum payment.

10.

Perpetual cash flow per year 60000

Interest rate 8%

So PV of perpetuity =60000/8%=$750,000

If the purchase cost if $500,000, then NPV of the perpetuity is $750,000-$500,000=$250.000

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