Statistics & Applications

Financial Math

Medium

applied

A machine costing ₹ 3,00,000 will have its scrap value of ₹ 50,000. The company at present plans to put ₹ 36,650 per annum at the end of each year in a sinking fund at the rate 5% per annum for the replacement of the machine after its useful life. Suppose the new machine will cost ₹ 4,00,000 at that time, then the useful life (approx.) of the machine is : [Given: $(1.4775)^{1/8} = 1.05$ ]

6.5 yrs

8.5 yrs

7 yrs

8 yrs

✅ Correct Option: 4

The company needs to buy a new machine for ₹4,00,000 but will receive ₹50,000 by selling the old machine as scrap.

Amount needed = ₹4,00,000 - ₹50,000

Amount needed = ₹3,50,000

The future value of a sinking fund with annual deposits is given by:

Future Value = Annual Deposit × $\dfrac{(1 + r)^n - 1}{r}$

where Future Value = ₹3,50,000, Annual Deposit = ₹36,650, and $r = 0.05$

Substituting the values:

$3,50,000 = 36,650 \times \dfrac{(1.05)^n - 1}{0.05}$

$\dfrac{3,50,000}{36,650} = \dfrac{(1.05)^n - 1}{0.05}$

$9.55 = \dfrac{(1.05)^n - 1}{0.05}$

$9.55 \times 0.05 = (1.05)^n - 1$

$0.4775 = (1.05)^n - 1$

$0.4775 + 1 = (1.05)^n$

$1.4775 = (1.05)^n$

The given information states that $(1.4775)^{1/8} = 1.05$

Raising both sides to the power of 8:

$[(1.4775)^{1/8}]^8 = (1.05)^8$

$1.4775 = (1.05)^8$

Comparing $1.4775 = (1.05)^n$ with $1.4775 = (1.05)^8$ :

$n = 8$

Therefore, the useful life of the machine is approximately 8 years.

2025: 29 May Shift 2

Every year the price of a motorcycle depreciates by Rs. 15000. After 12 years its price has become Rs. 50000. Then its original cost was:

2025: 21 May Shift 1

Anshu takes a personal loan of ₹10,00,000 at the rate of 12% per annum for 2 years, then the EMI by using flat rate method is

2025: 26 May Shift 2

At what rate will the present value of a perpetuity of Rs.1000 payable at the end of each quarter be Rs.50000?

2025: 14 May Shift 1

Which of the following are correct about the Sinking Fund?

(A) It is a fixed term account.

(B) It is a set-up for a particular upcoming expense.

(D) It can be used in any emergency.

Choose the correct answer from the options given below:

2026: 19 May Shift 1

The value of an item costing ₹ x depreciates in such a way that after 6 years the value is just a quarter of original value. The annual depreciation is:

2025: 13 May Shift 2

Which of the following statements about the Sinking Fund are correct?

(A) It is a fund established by a business entity by setting aside revenue over a period of time to fund a future capital expense.

(B) It is a fund established by a business entity by setting aside revenue over a period of time to fund a future repayment of a long-term debt.

(D) It is a fund that is accumulated for the purpose of paying off a financial obligation at some future designated date.

Choose the correct answer from the options given below:

Solution

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