Statistics & Applications

Financial Math

Medium

applied

A person has set up a sinking fund in order to have Rs. 10,00,000 after 10 years for his child education. The amount should put bi-annually into account paying 5% per annum compounded semi-annually is: [Given $(1.025)^{20} = 1.6386$ ]

Rs. 29148.14

Rs. 39148.14

Rs. 35148.14

Rs. 36148.14

✅ Correct Option: 2

The target amount (Future Value) is Rs. 10,00,000 after 10 years. The interest rate is 5% per annum compounded semi-annually, with deposits made bi-annually (twice a year).

Given: $(1.025)^{20} = 1.6386$

Since deposits and compounding occur twice a year:

Semi-annual interest rate: $r = \frac{5\%}{2} = 2.5\% = 0.025$

Number of periods: $n = 10 \times 2 = 20$ periods

For a sinking fund with regular deposits, the future value formula is:

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

where $P$ is the payment per period.

Rearranging to solve for $P$ :

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

$P = 10,00,000 \times \frac{0.025}{(1.025)^{20} - 1}$

Using the given value $(1.025)^{20} = 1.6386$ :

$P = 10,00,000 \times \frac{0.025}{1.6386 - 1}$

$P = 10,00,000 \times \frac{0.025}{0.6386}$

$P = \frac{25,000}{0.6386}$

$P = 39,148.14$

Therefore, the person should deposit Rs. 39,148.14 every 6 months.

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Choose the correct answer from the options given below:

A person has set up a sinking fund in order to have Rs. 10,00,000 after 10 years for his child education. The amount should put bi-annually into account paying 5% per annum compounded semi-annually is: [Given (1.025)20=1.6386(1.025)^{20} = 1.6386(1.025)20=1.6386]

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

A person has set up a sinking fund in order to have Rs. 10,00,000 after 10 years for his child education. The amount should put bi-annually into account paying 5% per annum compounded semi-annually is: [Given $(1.025)^{20} = 1.6386$ ]