PRESENT VALUE OF INSTALMENTS
The sum of the present values of all instalments of an instalment scheme is known as the present value of all instalments or present value of instalment scheme.
A person borrowed some money on compound interest and returned it in three years in equal annual instalments. If the rate of interest is 15% per annum and annual instalment is Rs. 486680,find the sum borrowed.
SOLUTION We have,
P = Value of each instalment = Rs 486680.
n = Number of instalments = 3
R = Rate of interest = 15% per annum compounded annually.
Sum borrowed Present value of all instalments
Sum borrowed = \( 100P/R { 1-(1+R/100)^-^n} \)
\( = 100*486680/15 {[1-(1+15/100) ^-^3 \) \( 48668000/15{1-(23/20)^-^3 \)INSTALMENTS
\( 48668000/15 * { 1-(20/23)^3} \) \( 48668000/15* (23^3-20^3) /(23)^3 \) \( 48668000/15*(12167-8000/12167) \) \( = 1111200. \)