Engineering Economics Blog

Table 1–1 details four different loan repayment plans described below. Each plan repays a $5000 loan in 5 years at 8% per year compound interest. 
 
• Plan 1: Pay all at end.  No interest or principal is paid until the end of year 5. Interest accumulates each year on the total of principal and all accrued interest. 
 
• Plan 2: Pay interest annually, principal repaid at end.  The accrued interest is paid each year, and the entire principal is repaid at the end of year 5. 

• Plan 3: Pay interest and portion of principal annually.  The accrued interest and one-fi  fth of the principal (or $1000) are repaid each year. The outstanding loan balance decreases each year, so the interest (column 2) for each year decreases. 
  
• Plan 4: Pay equal amount of interest and principal.  Equal payments are made each year with a portion going toward principal repayment and the remainder covering the accrued interest. Since the loan balance decreases at a rate slower than that in plan 3 due to the equal end-of-year payments, the interest decreases, but at a slower rate.   



(a)Make a statement about the   equivalence  of each plan at 8% compound interest. 
(b)Develop an 8% per year   simple  interest repayment plan for this loan using the same approach as plan 2. Comment on the total amounts repaid for the two plans. 
 
Solution 
 
(a) The amounts of the annual payments are different for each repayment schedule, and the total amounts repaid for most plans are different, even though each repayment plan  requires exactly 5 years. The difference in the total amounts repaid can be explained by the time value of money and by the partial repayment of principal prior to year 5.
    
A loan of $5000 at time 0 made at 8% per year compound interest is equivalent to each of the following:
  
    Plan 1   $7346.64 at the end of year 5 
    Plan 2   $400 per year for 4 years and $5400 at the end of year 5 
    Plan 3    Decreasing payments of interest and partial principal in years 1 ($1400) through 5 ($1080) 
    Plan 4   $1252.28 per year for 5 years   
  
An engineering economy study typically uses plan 4; interest is compounded, and a constant amount is paid each period. This amount covers accrued interest and a partial amount of principal repayment. 
 
(b)The repayment schedule for 8% per year simple interest is detailed in Table 1–2. Since the annual accrued interest of $400 is paid each year and the principal of $5000 is repaid in year 5, the schedule is exactly the same as that for 8% per year compound interest, and the total amount repaid is the same at $7000. In this unusual case, simple and compound interest result in the same total repayment amount. Any deviation from this schedule will cause the two plans and amounts to differ.