Question

ططط

genaun J 4) John Deere expects the cost of a tractor part to increase by S8 per year Agi yyc from now. If the cost in years 1-3 is S60, determine the present worth in yewraf the cas through year 10 at an interest rate of 12% per year. Draw your cash flow and shew all your steps in finding the solution (15 points) 5) Determine the nominal interest rate per year if the effective interest is 12 per year compounded quarterly.(15 points)

Answer 1

Question 4:

Year 0_______1_______2_______3_______4_______5_______6________7________8_______9_______10

↓             ↓              ↓              ↓ ↓ ↓ ↓               ↓             ↓              ↓         

Cost $60      $60          $60           $65            $70            $75           $80       $85 $90            $95

Present Worth in year 0 of costs in each year is ascertained using the formula

PV= C/(1+r)^t

Where PV= Present Value (in year 0), C= Cost in each year, r- rate of interest (given as 12%) and t is the relevant year .

Present Worth (in year 0) of cost each year is as follows:

AB 1 Rate of interest: 2 Year (t) Cost(C) DE F 12% Present Worth (1+r)^t c/(1+r)^t Cell ref Value Cell ref Value 1 $60 (1+C1) $60 (1+C1) A6 $60 (1+C1)^A7 $65 (1+C1) A8 $70 (1+C1)^A9 $75 (1+C1)^A10 $80 (1+C1) A11 $85 (1+C1) A12 $90 (1+C1)^A13 $95 (1+C1)^A14 1.12 B5/D5 1.2544 B6/D6 1.404928 B7/07 1.5735194 B8/D8 1.7623417 B9/D9 1.9738227 B10/D10 2.2106814 B11/D11 2.4759632 B12/D12 2.7730788 B13/D13 3.1058482 B14/D14 $53.571429 $47.831633 $42.706815 $41.308675 $39.719880 $37.997334 $36.187937 $34.330074 $32.454902 $30.587457

Question 5:

Effective interest rate=( (1+r)^n)-1 Where r= nominal rate for the period and n= number of compounding periods.

Given that Effective Interest Rate= 12%, Compounding is quarterly (n=4)

Therefore, 12%=( (1+r)^4)-1

(1+r)^4 = 1+12% = 1.12

(1+r) =      = 1.0287373

471.12

Nominal rate for quarter r = 1.0287373-1 = 0.0287373

Nominal rate per year= 0.0287373*4 = 0.11494938 Or, 11.494938%