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Q.(a) Find the effective rate which is equivalent to nominal rate of 10% p.a. compounded monthly. [Given that : (1⋅00833)12=1⋅1047(1 \cdot 00833)^{12} = 1 \cdot 1047]

(OR)
(b) Abhay bought a mobile phone for ₹ 30,000. The mobile phone is estimated to have a scrap value of ₹ 3,000 after a span of 3 years. Using the linear depreciation method, find the book value of the mobile phone at the end of 2 years.
CBSECBSE Class XII Board 2022Subjective· 2mImportance★★★★★
✓ Free question

  1. Effective rate =(1.00833)12−1=10.47%=(1.00833)^{12}-1=10.47\%.
  2. Straight-line depreciation of ₹9,000/year gives a book value of ₹12,000 after 2 years.

  1. Effective rate re=(1+rm)m−1r_e=\left(1+\dfrac{r}{m}\right)^{m}-1, where rr = nominal annual rate (decimal) and mm = number of compounding periods per year.
  2. Annual depreciation D=C−SnD=\dfrac{C-S}{n} and book value BVt=C−D⋅tBV_t = C - D\cdot t, where CC = cost, SS = scrap value, nn = useful life (years), tt = elapsed years.

Part (a): Effective rate for 10% p.a. compounded monthly.

  1. Nominal rate r=10%=0.10r=10\%=0.10; compounding periods m=12m=12 (monthly).
  2. Rate per month =rm=0.1012=0.00833=\dfrac{r}{m}=\dfrac{0.10}{12}=0.00833, so 1+rm=1.008331+\dfrac{r}{m}=1.00833.
  3. Effective rate re=(1.00833)12−1r_e=(1.00833)^{12}-1.
  4. Using the given value (1.00833)12=1.1047(1.00833)^{12}=1.1047: re=1.1047−1=0.1047r_e=1.1047-1=0.1047.
  5. As a percentage, re=10.47%r_e=10.47\%.

Part (b): Book value after 2 years (linear/straight-line depreciation).

  1. Cost C=₹30,000C=\text{₹}30{,}000; scrap value S=₹3,000S=\text{₹}3{,}000; useful life n=3n=3 years.
  2. Annual depreciation D=C−Sn=30000−30003=270003=₹9,000D=\dfrac{C-S}{n}=\dfrac{30000-3000}{3}=\dfrac{27000}{3}=\text{₹}9{,}000 per year.
  3. Total depreciation over 2 years =D×t=9000×2=₹18,000=D\times t = 9000\times 2 = \text{₹}18{,}000.
  4. Book value at end of 2 years =C−D⋅t=30000−18000=₹12,000=C - D\cdot t = 30000-18000=\text{₹}12{,}000.
✓Final answer

  1. Effective rate =10.47%=10.47\%
  2. Book value of the mobile phone at the end of 2 years =₹12,000=\text{₹}12{,}000

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