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In: Economics

please answer the following: 14- An infinite life project with initial cost of $35,250 and a...

please answer the following:

14- An infinite life project with initial cost of $35,250 and a maintenance cost of $12,260 starting at year x and repeating every x years. If interest rate = 6% and x=6, find the capitalized cost CC.

15-Find the future worth FW of an annual amount of $3,226 increasing every year by $660 for 10 years, interest rate = 11%.

16-Starting at year 1, an amount of $4,026 is deposited in an account of 3% interest every year for 7 years. Find the value of the present worth PW at year 0.

17- A deposit of $9,750 is made at year 4, find the value of the future worth FW at year 10 , interest=7%.

Solutions

Expert Solution

Question No-14

As per the question the question

Initial cost of the project = $35250

Maintenance cost of the project in every 6 year = $12260

Life of the project (N) = ∞ (infinite)

Rate of interest (i) = 6%

First we need to convert the recurring maintenance cost into EUAW for the first 6 year

Then A = $12260(A/F,6%,6)= $12260(0.14336)= $1757.5936

The perpetual maintenance cost of the project = $1757.5936(P/A,6%,∞)= $1757.5936/0.06

=$29293.2267

The capitalised cost of the project = initial cost of the project + perpetual maintenance cost of the project

The capitalised cost of the project = $35250+ 29293.2267 = $64543.2267 or Approx $64543.23

The capitalised cost of the project = $64543.23

Question No-15

As per the question the question

Annual amount (A1)=$3226

Increases every year (G) =$660

Period (N) = 10 years

Interest rate (i)=11%

A=A1+G(A/G,i,N)

A=3226+660(A/G,11%,10)

A=3226+660(3.6544)= 3226 +2411.904 =$5637.904

FV=$5637.904(F/A,11%,10)= $5637.904(16.72201)=$94277.087 or Approx $94277.09

The future value of the annual amount is = $94277.09

Question No-16

As per the question the question

Annual amount deposited (A)=$4026

Period of deposit (N) = 7 years

Interest rate (i)=3%

PW= $4026(P/A,3%,7)= $4026(6.23028)= $25083.1

Present worth of the deposit is = $25083.1

Question No-17

As per the question the question

Deposit made in the year 4 =$9750

Rate of interest = 7%

The future value of the deposit at year 10= ?

Interest bearing period of the deposit = 10-4 = 6 year

The future value = $9750(F/P,7%,6)= $9750(1.50073)=$14632.1175 or Approx $14632.12

The future worth of the deposit is = $14632.12

Rahul Sunny answered 6 months ago

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