Statistics & Applications

Financial Math

Medium

applied

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 )

Rs. 50,000

Rs. 40,000

Rs. 70,700

Rs. 67,500

✅ Correct Option: 4

House Price: Rs. 1,00,00,000

Down Payment (paid by mother): 20% of house price

Down Payment $= \dfrac{20}{100} \times 1,00,00,000$

Down Payment $= \text{Rs. } 20,00,000$

Loan Amount $= \text{House Price} - \text{Down Payment}$

Loan Amount $= 1,00,00,000 - 20,00,000$

Loan Amount $= \text{Rs. } 80,00,000$

Annual Interest Rate: 9% per annum

Monthly Interest Rate $= \dfrac{9\%}{12} = 0.75\% = 0.0075$

Time Period $= 25 \text{ years} = 25 \times 12 = 300 \text{ months}$

The EMI formula is:

$\text{EMI} = \dfrac{P \times r \times (1+r)^n}{(1+r)^n - 1}$

Where:

$P = 80,00,000$ (Principal)

$r = 0.0075$ (Monthly interest rate)

$n = 300$ (Number of months)

Substituting the values:

$\text{EMI} = \dfrac{80,00,000 \times 0.0075 \times (1.0075)^{300}}{(1.0075)^{300} - 1}$

Given $(1.0075)^{300} = 9$ :

$\text{EMI} = \dfrac{80,00,000 \times 0.0075 \times 9}{9 - 1}$

$\text{EMI} = \dfrac{6,00,000 \times 9}{8}$

$\text{EMI} = \dfrac{54,00,000}{8}$

$\text{EMI} = \text{Rs. } 67,500$

Therefore, the EMI paid by Rakshita is Rs. 67,500.

2025: 19 May Shift 1

Mr. Mittal invested Rs. 20,000 in a mutual fund in the year 2019. The value of the mutual fund increased to Rs. 32,000 in the year 2024. The compound annual growth rate of his investment is:

[Given $(1.6)^{1/5} = 1.098$ ]

2026: 21 May Shift 2

Geetansh invested ₹27,000 and it grows to ₹81,000 in 2 years. The CAGR % will be:

2025: 3 June Shift 2

Ram invested Rs.20,000 in a mutual fund in the year 2012. The value of the mutual fund increased to Rs.32,000 in the year 2017, then the compound annual growth rate of his investment is (Given that $(1.6)^{\frac{1}{5}} = 1.098$ )

2026: 30 May Shift 1

In reference to the financial mathematics, which of the following statements are correct?

A. Sinking fund is an annuity created for accumulating money that can be used for paying off a financial obligation at some future pre-decided date.

B. The compound annual growth rate (CAGR) is calculated by dividing the cumulative return by the number of years.

C. The average annual growth rate (AAGR) is linear measure that does not account for the effects of compounding.

D. Sinking fund is created to deposit surplus money which can be used for any future need.

Choose the correct answer from the options given below:

2025: 27 May Shift 1

As per the graph given below:

Match List-I with List-II

List-I	List-II
(Function/Area/point)	(Representation)
(A) Consumers Surplus	(I) y=g(x)
(B) Supply function	(II) v
(C) Demand function	(III) s
(D) Equilibrium point	(IV) y=f(x)

Choose the correct answer from the options given below:

2025: 16 May Shift 1

If $C$ is the original value of the asset, $S$ is the scrap value, n is the useful life of the asset and $D$ is the annual depreciation, then

Solution

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