How much amount is required to be invested every year so as to accumulate ₹ 3,00,000 at the end of 10 years, if interest is compounded annually at 10%? (a) ₹ 18,823.65 (b) ₹ 18,828.65 (c) ₹ 18,832.65 (d) ₹ 18,882.65?

Question

Answer

Solution:

To find the amount required to be invested every year to accumulate ₹ 3,00,000 at the end of 10 years with 10% annual interest compounded annually, we can use the formula for the future value of an annuity:

FV = P[((1 + r)^n - 1) / r]

where FV is the future value, P is the periodic payment or the amount to be invested every year, r is the annual interest rate as a decimal, and n is the number of periods or years.

Substituting the given values, we get:

₹ 3,00,000 = P[((1 + 0.1)^10 - 1) / 0.1]

Simplifying the expression inside the bracket:

₹ 3,00,000 = P[(1.1^10 - 1) / 0.1]

₹ 3,00,000 = P[2.5937]

P = ₹ 3,00,000 / 2.5937

P = ₹ 1,15,766.50 (rounded off to the nearest paisa)

Therefore, the amount required to be invested every year to accumulate ₹ 3,00,000 at the end of 10 years with 10% annual interest compounded annually is ₹ 1,15,766.50.

Answer: (e) None of the above. The correct answer is ₹ 1,15,766.50.

Answer

Step 1: Understand the problem
We need to find the amount to be invested every year so that at the end of 10 years, the total accumulated amount is Rs. 3,00,000 with an annual interest rate of 10% compounded annually.

Step 2: Use the formula for the future value of an ordinary annuity
The future value of an ordinary annuity formula is:
FV = P * [(1 + r)^n - 1] / r

Where:
FV = Future value of the annuity
P = Annual payment (amount to be invested every year)
r = Interest rate per period (annual interest rate)
n = Number of periods (number of years)

Step 3: Plug in the values and solve for P
We know the future value (FV) should be Rs. 3,00,000, the interest rate (r) is 10% or 0.1, and the number of periods (n) is 10 years. We need to find the annual payment (P).

3,00,000 = P * [(1 + 0.1)^10 - 1] / 0.1

Step 4: Solve the equation for P
First, calculate the value inside the brackets:
(1 + 0.1)^10 - 1 = 1.1^10 - 1 ≈ 1.5937

Now, divide by the interest rate (0.1):
1.5937 / 0.1 = 15.937

Finally, solve for P:
3,00,000 = P * 15.937
P = 3,00,000 / 15.937
P ≈ 18,826.45

So, the amount to be invested every year is approximately Rs. 18,826.45.

Answer

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Answer

How much amount is required to be invested every year so as to accumulate ₹ 3,00,000 at the end of 10 years, if interest is compounded annually at 10 % ? [Give (1.1)10 = 2.5937]How much amount is required to be invested every year so as to accumulate ₹ 3,00,000 at the end of 10 years, if interest is compounded annually at 10 % ? [Give (1.1)10 = 2.5937]

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