ON FINDING THE NUMBER OF INSTALMENTS
EXAMPLE What annual payment will discharge a debt of Rs. 5082 due in 2 years at 10% r annum compounded annually?
SOLUTION Let the value of each annual instalment be Rs. P. We have,
R = Rate of interest = 10% per annum compounded annually
n = Number of instalments = 2.
Present value of all instalments = \( Rs.100P/R {1-(1+R/100)^-^n \)
Also,
Present value of Rs. 5082 due in 2 years
\( Rs. {5082/(1+R/100)^2} \) \( = Rs.5082/(1+10/100)^2) \) \( = Rs.5082*100/121 = 4200 \)Present value of all instalment = Present value of Rs. 50282 due in 2 years.
\( 210/121*P = 4200 \) \( P= 121*20 = 2420 \)Hence, value of each instalment = Rs. 2420.