Statistics & Applications

Financial Math

Medium

applied

A company purchased a machine for ₹ 15,00,000 and its effective life is estimated to be 10 years. A sinking fund is created for replacing the machine at the end of its effective life when its scrap value is ₹ 2,42,000. What amount company should provide, at the end of every year out of profits for the sinking fund if it accumulates an interest of 5% per annum? [Given(1.05)¹⁰=1.629]

₹ 6,2900

₹ 1,00,000

₹ 1,20,000

₹ 1,06,290

✅ Correct Option: 2

The company wants to save money every year so that after 10 years, they have enough to buy a new machine.

Given:

New machine cost: ₹15,00,000
Scrap value: ₹2,42,000
Years to save: 10 years
Interest rate: 5% per annum
$(1.05)^{10} = 1.629$

The company will get some money by selling the old machine (scrap value), so they don't need to save the full ₹15,00,000.

Amount needed from savings $=$ New machine cost $-$ Scrap value

$= ₹15,00,000 - ₹2,42,000$

$= ₹12,58,000$

When depositing the same amount every year with interest, the future value formula is:

Future Value $= \text{Annual Payment} \times \dfrac{(1+r)^n - 1}{r}$

Where:

Future Value $= ₹12,58,000$
Annual Payment $= P$ (to be found)
$r = 0.05$
$n = 10$ years

$₹12,58,000 = P \times \dfrac{(1.05)^{10} - 1}{0.05}$

$₹12,58,000 = P \times \dfrac{1.629 - 1}{0.05}$

$₹12,58,000 = P \times \dfrac{0.629}{0.05}$

$₹12,58,000 = P \times 12.58$

$P = \dfrac{₹12,58,000}{12.58}$

$P = ₹1,00,000$

Therefore, the company should provide ₹1,00,000 at the end of every year.

2026: 30 May Shift 2

A man wants to get ₹10,000 forever at the beginning of each quarter, if the money is worth 8% per annum compounded quarterly, then the money he needed to invest now is

2026: 15 May Shift 1

Which of the following statements are correct about the compound annual growth rate (CAGR) ?

A. CAGR is a compounded annual return of an investment.

B. CAGR is calculated by using the final and beginning value of an investment.

C. CAGR can be used to calculate and communicate the average growth of a single investment.

D. CAGR can be used to demonstrate and compare the performance of investment advisors.

Choose the correct answer from the options given below:

2026: 30 May Shift 2

Which of the following is correct about the sinking fund?

2025: 15 May Shift 2

Which of the following are similarities between the sinking fund and the savings account?

(A) The sinking fund and the savings account are both financial tools.

(B) Both can be used in any emergency.

(D) Both are long-term accounts which can be closed any time.

Choose the correct answer from the options given below:

2025: 2 June Shift 1

A machine costing Rs 50,000 has a useful life of 4 years.The estimated scrap value is Rs 10,000 . The rate of depreciation per annum is:

2026: 30 May Shift 1

An electric bike costs ₹42,000 and has a useful life of 10 years. If annual depriciation is ₹3,000, then the scrap value by using linear method of depriciation is:

Solution

Related questions:

Keyboard Shortcuts

CUET Mathematics Past Year Questions (Topic-Wise)