Equal-Payment Series Capital Recovery Method
Equal-Payment Series Capital Recovery
The objective of this mode of investment is to
find the annual equivalent amount (A) which is to be recovered at the end of
every interest period for n interest periods for a loan (P) which is sanctioned
now at an interest rate of i compounded at the end of every interest period
Cash flow diagram of equal-payment series capital recovery amount
Here,
P = present worth (loan amount)
A = annual equivalent payment (recovery
amount)
i = interest rate
n = No. of interest periods
The formula to compute P is as follows:
A = P i(1
+ i)n / (1 + i)n – 1 = P (A/P, i, n)
Where,
(A/P, i,
n) is called equal-payment series capital recovery factor.
Example problem on equal-payment series capital recovery
A company takes a loan of Rs 35,00,000 to
modernize its boiler sections. The loan is to be repaid in 25 equal
installments at 10 % interest rate compounded annually. Find the equal
installment amount that should be paid for the next 25 years.
Given data
P = Rs. 35,00,000
i = 10%
n = 25 years
To find
A
Formula used
A = P (A/P,
i, n)
Solution
A = P (A/P, i, n)
= 35,00,000 (A/P, 10%, 25)
= 35,00,000 * 0.1102
A = Rs. 3,85,700
Result
The company should pay
an equal amount Rs. 3,85,700 at the end of every year for the next 20 years at
an interest rate of 10% to repay the loan Rs. 35,00,000.
