Statistics & Applications

Financial Math

Medium

applied

Mr. X invested Rs. 4,00,000 in shares for 5 years. The value of this investment was Rs. 4,50,000 at the end of the second year, Rs. 490000 at the end of the third year and on maturity, the final value stood at Rs. 6,00,000. The compound annual growth rate of this investment is:

[Given that: $(1.5)^{1/5} = 1.084]$

8.4 %

10.8 %

9.084 %

11 %

✅ Correct Option: 1

CAGR (Compound Annual Growth Rate) tells you the single steady rate at which an investment would have grown per year, if it grew at the same rate every year from start to finish. The formula is:

$CAGR = \left(\dfrac{\text{Final Value}}{\text{Initial Value}}\right)^{\dfrac{1}{n}} - 1$

where $n$ is the number of years.

Here, Initial Value $= Rs.\;4,00,000$ , Final Value $= Rs.\;6,00,000$ , and $n = 5$ years.

$CAGR = \left(\dfrac{6,00,000}{4,00,000}\right)^{\dfrac{1}{5}} - 1$

$CAGR = (1.5)^{\frac{1}{5}} - 1$

Using the hint given in the question, $(1.5)^{1/5} = 1.084$

$CAGR = 1.084 - 1 = 0.084$

Converting to percentage:

$CAGR = 0.084 \times 100 = 8.4\%$

2025: 29 May Shift 2

Rakshita plans to buy a house for Rs.1,00,00,000 with down payment of 20% of the value of house paid by her mother, Rest of the amount she wishes to pay in 25 years by equal monthly installment at an interest of 9% per annum compounded monthly. Then the EMI paid by her is: (Given $(1.0075)^{300}$ = 9 )

2024: 16 May Shift 1

For an investment, if the nominal rate of interest is $10 \%$ compounded half yearly, then the effective rate of interest is :

2025: 3 June Shift 1

The effective rate, which is equivalent to a nominal rate of 12% compounded semi-annually, is

2025: 22 May Shift 2

At what rate of interest will the present value of a perpetuity of ₹ 500 payable at the end of every 6 months be ₹ 20,000?

2026: 30 May Shift 2

Scrap value of a machine is one-tenth of its actual cost. If the estimated life of the machine is ten years and the annual depreciation under linear method is ₹45000, then the cost of the machine is

2025: 27 May Shift 1

Mohini purchases a house worth Rs. 50 lakhs and makes a down payment of Rs. 11.2 lakhs. She pays the remaining amount on monthly EMI using a reducing balance method. The bank charges 6% per annum compounded monthly for a tenure of 25 years. Her EMI is:

[Given: $(1.005)^{-300} \approx 0.224$ ]

Solution

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