Question

2.

a)

The value of a 8 year lease that requires payments of $850 made at the beginning of every quarter is $25,000. What is the nominal interest rate compounded quarterly? % Round to two decimal places

b)

Answer 1

No of quarters (n)= 8*4=   32  
Present value=   25000  
      
Present value of annuity due = Annuity + Annuity * (1 - (1/(1+i)^(n-1))/i       
      
      
25000 = 850 +850*(1-(1/(1+i)^(32-1)))/i       
i will be calculated by trial and error method      
Assume i=0.5% or   0.005  
850 +850*(1-(1/(1+0.005)^(32-1)))/0.005      
25203.17997      
      
Assume i= 0.6% or   0.006  
850 +850*(1-(1/(1+0.006)^(32-1)))/0.006      
24829.1841      
interpolation formula = lower rate +((uper rate - lower rate)*(Uper price - bond actual price)/(uper price - lower price))      
0.5% +((0.6%-0.5%)*(25203.17997-25000)/(25203.17997-24829.1841))      
      
0.005543267951      
Annual rate = 0.005543267951*12=   0.06651921541  
or 6.65%      
So Nominal ínterest rate is 6.65%      
      

B.

Future value =   11000
Time in months (n) =   12
interest rate Monthly (i)= 2.12%/12=   0.001766666667
  
Future value of ordinary annuity formula = P *{ (1+i)^n - 1 } /i  
11000 = P*(((1+0.0017666667)^12)-1)/0.001766667  
P=11000/   12.11728938
=$907.7937857  

So deposit every month is $907.79

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