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Homework answers / question archive / A 10-year loan of $3,000 is arranged to be settled by payments at the end of each year

A 10-year loan of $3,000 is arranged to be settled by payments at the end of each year

Finance

A 10-year loan of $3,000 is arranged to be settled by payments at the end of each year. It can be repaid under the following two options: i. Equal annual payments at an annual effective rate of 5.50%. ii. Installments of $300 each year plus interest on the unpaid balance at an annual effective rate of i. The sum of the payments under option (i) equals the sum of the payments under option (ii). Find i.

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  loan amount 3000  
       
  option 1 equal anuual payments
  interst rate 5.50%  
       
  EAI = P × r × (1 + r)n/((1 + r)n - 1) where P= Loan amount, r= interest rate, n=tenure in number of years    
  3000*0.055*(1+0.055)^10/((1+0.055)^10-1)  
  398.0033061    
  total amount paid 3980.03306  
       
  Option 2    
       
year opening amt principle paid interest
1 3000 300 3000*i
2 2700 300 2700*i
3 2400 300 2400*i
4 2100 300 2100*i
5 1800 300 1800*i
6 1500 300 1500*i
7 1200 300 1200*i
8 900 300 900*i
9 600 300 600*i
10 300 300 300*i
  Total 3000 16500*i
       
  total in option 1 and option 2 are same    
  3980=3000+16500*i    
  16500*i=980    
  i=980/16500    
i= 0.059393939    
  i.e. 5.9393    
  5.94%    
       

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