EECE

Ahmad Aljumah EECE 490B Norm Galassi Homework #4 Problem 4.2:

- The present worth of an investment is the sum of the present value of the cash outflows and cash inflows.

Present worth of the raise = 10,000(P/A,I,n) where A is the amount of the raise, i is the interest rate, and n is the number of years. = 116,550

- Future worth is the worth of the amount at any future time, Future worth of the raise = 10,000(F/A,i,n) =1,723,170 Problem 4.16

a) PW(B) = 200(P/A,10%,4) =634 b) FW(C)= [A(F/A,i,n)](F/P,i,n) ==55.051 c) PW(V)=F(F/P,i,n) =228.13

Problem 4.32:

- A mortgage basically refers to the loan pertaining to which real estate or property is taken into consideration as collateral. Thus the borrower is required to enter into contract with the bank or lender. Therefore borrower gets cash in lieu of the collateral security for which the payment is required to be made in specific period along with underlying interest.

- JC is planning to own a house. Thus she is required to have at least 20% of the cost of

home as down payment. Since, she is available with $600 monthly after paying for all the expenses. However the amount available pertaining to the mortgage is required to be reduced by at least $100 in order to discharge liability towards real estate taxes and home insurance. Therefore the computation of the loan available to JC at 3% interest for period of 30 years using spreadsheet function ​JC can afford a loan of 118,595

- .The down payment for the loan is 20% of the total cost of the house and the remaining

80% is paid through mortgage. Price of the house would be 148244 Hence, it is ascertained that the price of house accounts for JC must save for the closing costs and down payment for the home. Therefore, ​JC’s savings is computed as 33,149$

Problem 4.45:

- "Cash-flow moment-equation: The cash-flow moment-equation is the equation which shows the equilibrium point at any given pivot point. Thus the distance from the pivot points will be the number of years and distance from the right side of the pivot point is the positive forces. However distance from the left side of the pivot point on the other hand is the negative forces which will be discounted

- .In this case, year 4 has been taken as pivot point. The distance from point 4 is 0,

distance from point 2 is 1 and distance from point 1 is 2. These are the points situated at right side of the pivot point. Hence, the value will be positive. These values will be compounded. 0= (compounded values of the right side cash flows - discounted values of the left side cash flows)

- .In this case, year 5 has been taken as pivot point. The distance from point 3 is 2, distance from point 2 is 3 and distance from point 1 is 4. These are the points situated at right side of the pivot point with upside direction. Hence, the value will be positive. These values will be compounded. The distance from point 5 is -1. These are the points situated at left side of the pivot point with downside direction. Hence, the value will be negative. These values will be discounted. =(10 x (1+i)^4 + 10 x(1+i)^2=C x (1+i)^-1)

- In this case, year 5 has been taken as pivot point. The distance from point 3 is 2,

distance from point 2 is 3 and distance from point 1 is 4. These are the points situated at right side of the pivot point with upside direction. Hence, the value will be positive. These values will be compounded. Since there exist no points at left side of the pivot point. Thus, the value will not be negative as result there will be no discounted value.

Problem 4.48

- Capital Recovery factor, [i(1+i)^n / (1+i)^n -1 =0.1408 - Sinking Fund Factor, [i/(1+i)$n -1] =0.0408

Subtract the two equations to get the interest rate as 10% after substituting, the value of the time period n is 13. Problem 4.52:

- a) P= [A(P/A,i,n) + G(P/G,i,n)](P/F, i,n) =2,189.1128

- b) P = 2,058.566 Following the formula to calculate the uniform amount for all 5 years A=P(A/P,i,n) =543$

- c) P =1,887$ Problem 4.74:

- Sales in the first year are $60,000. Sales in the subsequent years increase by 8% (or 0.08) each year. It is given that the interest rate is 10% (or 0.10) and the total number of years is 15. This is a geometric gradient cash flow series where the first cash flow (A) is $60,000 and the geometric gradient (g) is 0.08. Therefore, the present worth of the sales is $721,800.

Problem 4.88:

- The annuity is calculated on the basis if the annuity factor of the present value. A=p(annuity factor) =278$

- The nominal annual interest rate is the product if monthly interest rate. = Monthly intrest

rate x Number of months =15% - The effective annual interest rate is 16.08%

Problem 4.118:

- The future worth of the annuity can be calculated as below: F= 3000(F/A,1.5%,12) = 39,123$