Statistics & Applications

Financial Math

Medium

applied

A person has purchased a home for Rs.10,00,000 with down payment of Rs 2,00,000. He amortize the balance at 9% per annum compounded monthly for 25 years then the equal monthly installment (EMI) is:

[Given that: $\frac{(1.0075)^{300} - 1}{(.0075)(1.0075)^{300}} = 119.1616]$

Rs 8174.55

Rs 6713.57

Rs 7248.64

Rs 7534.25

✅ Correct Option: 2

The loan amount is the home price minus the down payment:

Loan Amount (P) = Rs. 10,00,000 - Rs. 2,00,000

P = Rs. 8,00,000

The interest details are:

Annual Interest Rate = 9% per annum

Monthly Interest Rate (r) = 9% ÷ 12 = 0.75% = 0.0075

Time Period = 25 years = 25 × 12 = 300 months (n)

The EMI formula is:

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

Where P = 8,00,000, r = 0.0075, and n = 300

The given expression $\frac{(1.0075)^{300} - 1}{(0.0075)(1.0075)^{300}} = 119.1616$ is the reciprocal of the term needed in the EMI formula.

Therefore:

$\frac{(0.0075)(1.0075)^{300}}{(1.0075)^{300} - 1} = \frac{1}{119.1616}$

Substituting into the EMI formula:

$\text{EMI} = 8,00,000 \times \frac{1}{119.1616}$

$\text{EMI} = \frac{8,00,000}{119.1616}$

$\text{EMI} = 6713.57$

Therefore, the equal monthly installment is Rs. 6713.57

2026: 26 May Shift 2

Which of the following are the true?

A. The cost of Rs.7200 , 8% stock at Rs.90 is Rs.6480.

B. The cost of Rs.4500 , 8.5% stock at 4% premium is Rs.4680.

C. The cost of Rs.6400 , 10% stock at 15% discount is Rs.5440.

D. The cost of Rs.7200 , 8% stock at Rs.90 is Rs.5961.60.

Choose the correct answer from the options given below:

2026: 26 May Shift 2

Let us denotes R=Periodic payment,i=interest per period per rupee ,n=number of payment,P=pricipal payment

Match the terms in List I with their respective formula in List II.

LIST-I	LIST-II
A. The amount in a sinking fund after $n$ period with payment at end	I. $\dfrac{Pi(1+i)^n}{(1+i)^n - 1}$
B. EMI by using flat rate method	II. $P\left(i + \dfrac{1}{n}\right)$
C. The amount in a sinking fund after $n$ period with payment at beginning	III. $R\left\{\dfrac{(1+i)^n - 1}{i}\right\}$
D. EMI by using reducing balance payment rate method	IV. $R(1+i)\left[\dfrac{(1+i)^n - 1}{i}\right]$

Choose the correct answer from the options given below:

2025: 21 May Shift 2

Which of the following statements are correct?

(A) A fund which is created to accumulate money over the years to discharge a future obligation is called a sinking fund.

(B) The amount or future value of perpetuity is well-defined.

(D) An equated monthly installment is a fixed payment made by a borrower to a lender at a specific date every month to clear off the loan.

Choose the correct answer from the options given below:

2026: 30 May Shift 1

Amayra takes a loan of ₹5,00,000 at an interest of 10% per annum for a period of three years. The equated monthly installment (EMI) by using flat rate method, she has to pay is:

2025: 22 May Shift 2

Rahul invested ₹ 20000 in a mutual fund in year 2018. If the value of mutual fund increased to ₹ 32000 in year 2023. Then the compound annual growth rate of his investment is: $[given \, that(1.6)^{1/5} = 1.098]$

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:

Solution

Related questions:

Keyboard Shortcuts

CUET Mathematics Past Year Questions (Topic-Wise)