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A) Calculate the amount Mr. Ram will receive after 5 years. b) Calculate the present value of the annuity.

Business/Management

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2 parts
a

Rs. 81,930.82\text{Rs. } 81,930.82

b

Rs. 123,342.24\text{Rs. } 123,342.24

Step-by-step solution

4 steps

Here are the calculations for question 11:

Part a· 2 steps

Calculate the amount Mr. Ram will receive after 5 years.

  1. Identify the given values.

    Principal (P)=Rs. 50,000(P) = \text{Rs. } 50,000
    Annual interest rate (r)=10%=0.10(r) = 10\% = 0.10
    Compounding frequency (n)=4(n) = 4 (quarterly)
    Time (t)=5(t) = 5 years

  2. Use the compound interest formula.

    The formula for the future value with compound interest is:

    A=P(1+rn)ntA = P \left(1 + \frac{r}{n}\right)^{nt}

    Substitute the values:

    A=50,000(1+0.104)4×5A = 50,000 \left(1 + \frac{0.10}{4}\right)^{4 \times 5} A=50,000(1+0.025)20A = 50,000 (1 + 0.025)^{20} A=50,000(1.025)20A = 50,000 (1.025)^{20} A=50,000×1.63861644A = 50,000 \times 1.63861644 A=81,930.82A = 81,930.82

    The amount Mr. Ram will receive after 5 years is Rs. 81,930.82\boxed{\text{Rs. } 81,930.82}.

Part b

Rs. 123,342.24\text{Rs. } 123,342.24

Calculate the present value of the annuity.

  1. Identify the given values.

    Annuity payment (PMT)=Rs. 30,000(PMT) = \text{Rs. } 30,000 per year
    Number of years (t)=6(t) = 6 years
    Discount rate (r)=12%=0.12(r) = 12\% = 0.12

  2. Use the present value of an ordinary annuity formula.

    The formula for the present value of an ordinary annuity is:

    PV=PMT×[1−(1+r)−tr]PV = PMT \times \left[ \frac{1 - (1 + r)^{-t}}{r} \right]

    Substitute the values:

    PV=30,000×[1−(1+0.12)−60.12]PV = 30,000 \times \left[ \frac{1 - (1 + 0.12)^{-6}}{0.12} \right] PV=30,000×[1−(1.12)−60.12]PV = 30,000 \times \left[ \frac{1 - (1.12)^{-6}}{0.12} \right] PV=30,000×[1−0.5066310.12]PV = 30,000 \times \left[ \frac{1 - 0.506631}{0.12} \right] PV=30,000×[0.4933690.12]PV = 30,000 \times \left[ \frac{0.493369}{0.12} \right] PV=30,000×4.111408PV = 30,000 \times 4.111408 PV=123,342.24PV = 123,342.24

    The present value of the annuity is Rs. 123,342.24\boxed{\text{Rs. } 123,342.24}.

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