Which of the following statements is true?
A. EMI in flat rate method, \(\mathrm{EMI} = \displaystyle\frac{\text{Principal} + \text{Interest}}{\text{Number of Payment}}\)
B. EMI in reducing balance method, \(\mathrm{EMI} = P \times \displaystyle\frac{i}{1 + (1 + i)^n}\) where P = Principal, i = interest rate, n = no. of payments
C. In sinking fund, a fixed amount at regular intervals is deposited.
D. Approximate Yield to Maturity \(= \displaystyle\frac{\text{Coupon Payment} + \frac{\text{Face Value} + \text{Present Value}}{\text{Number of Payment}}}{\frac{\text{Face Value} + \text{Present Value}}{2}}\)
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → A and C only
The standard formulas, with P = principal, i = interest rate per period, n = number of payments, C = coupon payment, F = face value and V = present value:
\( \displaystyle \text{flat rate: } \mathrm{EMI} = \frac{P + \text{Interest}}{n} \)
\( \displaystyle \text{reducing balance: } \mathrm{EMI} = P \times \frac{i}{1 - (1 + i)^{-n}} \)
\( \displaystyle \text{approximate YTM} = \frac{C + \frac{F - V}{n}}{\frac{F + V}{2}} \)
So the flat-rate formula is as stated, the reducing-balance denominator must be \(1 - (1 + i)^{-n}\), a sinking fund is built from fixed regular deposits, and the YTM numerator uses F − V, not F + V.
Checking the statements
(A) EMI in flat rate method, \(\mathrm{EMI} = \frac{\text{Principal} + \text{Interest}}{\text{Number of Payment}}\) — Correct. Total amount repaid shared equally among the payments.
(B) EMI in reducing balance method, \(\mathrm{EMI} = P \times \frac{i}{1 + (1 + i)^n}\) — Incorrect. The denominator is \(1 - (1 + i)^{-n}\), not \(1 + (1 + i)^n\).
(C) In sinking fund, a fixed amount at regular intervals is deposited. — Correct. This is how a sinking fund is built up.
(D) Approximate Yield to Maturity with Face Value + Present Value in the numerator — Incorrect. The numerator has (Face Value − Present Value) ÷ Number of Payment.