Statistics & Applications

Financial Math

Medium

applied

The amount should be deposited at the end of every 6 months to accumulate Rs.50,000 in 8 years if money is worth 6% p.a. compounded semiannually, is: [Given $(1.03)^{16} = 1.6047$ ]

Rs. 3432.53

Rs. 2783.08

Rs. 2480.57

Rs. 2149.93

✅ Correct Option: 3

Given information:

Future Value = Rs. 50,000
Time Period = 8 years
Interest Rate = 6% per annum compounded semiannually
$(1.03)^{16} = 1.6047$

Converting to semiannual terms:

Interest rate per 6 months:

$i = \frac{6\%}{2} = 3\% = 0.03$

Number of deposits:

$n = 8 \times 2 = 16$

The future value of annuity formula:

$FV = P \times \frac{(1+i)^n - 1}{i}$

Rearranging for $P$ :

$P = FV \times \frac{i}{(1+i)^n - 1}$

Substituting the values:

$P = 50,000 \times \frac{0.03}{(1.03)^{16} - 1}$

Using $(1.03)^{16} = 1.6047$ :

$P = 50,000 \times \frac{0.03}{1.6047 - 1}$

$P = 50,000 \times \frac{0.03}{0.6047}$

Computing the numerator:

$50,000 \times 0.03 = 1,500$

Dividing by the denominator:

$P = \frac{1,500}{0.6047}$

$P = 2,480.57$

The amount to be deposited at the end of every 6 months is Rs. 2,480.57

2025: 26 May Shift 2

Vatsala buys a car for Rs.7,00,000 and pays upfront Rs.2,50,000 through her credit card. The balance is to be paid in 5 years by equal monthly installments at an interest of 7% per annum as reducing balance. The EMI to be paid by Vatsala will be :- [given (1.0058)⁻⁶⁰=0.7068]

2025: 15 May Shift 1

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

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: 19 May Shift 2

An electric scooter costs ₹ 36,000 and has a useful life of 15 years. If annual depreciation is ₹ 2,000, Its scrap value by using linear method of depreciation is:

2025: 30 May Shift 2

Ram wishes to purchase a house for ₹ 15,00,000 and made a down payment of ₹ 5,00,000. If he can amortize the balance at 9% per annum compounded monthly for 25 years, then his EMI is:

[Given $(1.0075)^{300} ≈ 9.41$ ]

2025: 19 May Shift 1

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

The amount should be deposited at the end of every 6 months to accumulate Rs.50,000 in 8 years if money is worth 6% p.a. compounded semiannually, is: [Given (1.03)16=1.6047(1.03)^{16} = 1.6047(1.03)16=1.6047]

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

The amount should be deposited at the end of every 6 months to accumulate Rs.50,000 in 8 years if money is worth 6% p.a. compounded semiannually, is: [Given $(1.03)^{16} = 1.6047$ ]