Question 11.I.A.1 (Cash Down Payment): Under a hire-purchase deal structured by the Hypothetical Fi......
Under a hire-purchase deal structured by the Hypothetical Finance Ltd (HFL) for the Hypothetical Industries Ltd. (HIL), the (flat) rate of interest is 15 per cent. The HIL is required to make a cash down payment of 25 per cent and the repayment of the loan is to be made in 36 equated monthly instalments. On the assumption of payment of instalment in (a) advance (b) arrear, compute the ERI/APR for the plan.
The ERI/APR can be computed (A) by using the approximation formula or (B) by applying the trial and error approach.
\, (A) Approximation Approach/Formula
\, (a) Computation of APR/ERI (Payment in Arrear)
\qquad\qquad\,I = APR/ERI
\qquad\qquad\,N = Number of payments
\qquad\qquad\,F = Flat rate of interest per unit time
\qquad\qquad\quad =\frac{36}{37} × 2 × 0.15 = 0.292 = 29.2 per cent
\, (b) Computation of APR/ERI (Payment in Advance)
\qquad\qquad I=\frac{N}{N+1}× 2F=\frac{36}{37} × 2 × 0.15 = 0.0309 = 30.9 per cent
\, (B) Trial and Error Approach (Assumed Amount of Rs 1,000)
\, (a) Computation of APR/ERI (Payment in Arrear):
\, Amount of loan (0.75 × Rs 1,000) = Rs 750
\, Total credit charge = Rs 750 × 0.15 – × Rs 337.5
\, Equated monthly instalment = [Rs 1,087.5 (Rs 750 + Rs 337.5)] ÷ 36
\, = Rs 30.21
\, The value of I (APR) is given by the equation:
\, (Rs 30.21 × 12) × PVIFA_\mathrm{m} (I,3) = Rs 750
\, = 362.52 × \frac{I}{I^{(12)}} × PVIFA (I,3) = Rs 750
\, By trial and error and interpolation,
\, I – 29.4 per cent
\, (b) Computation of IPR/ERI (Payment in Advance):
\, The value of I an be obtained by the equation: (30.31 × 12) PVIFA_\mathrm{m}
\, (I,3) = Rs 750
\, By trial and error and interpolation: I = 31.2 per cent