Statistics & Applications

Financial Math

Easy

applied

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

$10.25 \%$

$11.25 \%$

$10.125 \%$

$11.025 \%$

✅ Correct Option: 1

Effective rate $= \left(1 + \frac{r}{n}\right)^n - 1$

Where:

$r$ $r$ = nominal interest rate (as a decimal)
- $n$ = number of compounding periods per year

Given:

Nominal rate = 10% = 0.10
- Compounding = half-yearly, so $n = 2$

Effective rate

$= \left(1 + \frac{0.10}{2}\right)^2 - 1$

$= \left(1 + 0.05\right)^2 - 1$

$= (1.05)^2 - 1$

$= 1.1025 - 1$

$= 0.1025$

$= 10.25\%$

2024: 16 May Shift 1

A flower vase costs ₹ $36,000$ . With an annual depreciation of ₹ $2,000$ , its cost will be ₹ $6,000$ in $_____$ years.

2025: 21 May Shift 1

What sum of money is needed to invest now, so as to get ₹5000 at the beginning of every month forever, if the money is worth 6% per annum compounded monthly?

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

2026: 25 May Shift 1

A company has issued a bond of face value ₹ 90,000 carrying an annual dividend of 7% and maturing in 15 years. If the prevailing market rate of interest is 9% , the value of bond redeemed at par is: (given $(1.09)^{-15} \approx 0.3$ )

2026: 18 May Shift 2

A father has setup a sinking fund in order to have ₹ 2,40,000 after 10 years for his daughter's marriage. How much amount should he set aside bi-annually into an account paying 5% per annum compounded half-yearly?

[given : $(1.025)^{20}\approx 1.6$ ]

2026: 12 May Shift 2

Rama takes a personal loan for a car worth ₹5,00,000 at an interest rate of 7% per annum to be repaid by equal monthly instalments (EMI) in 5 years. Using flat rate method, EMI will be:-

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

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

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