Statistics & Applications

Financial Math

Medium

applied

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?

₹10,00,500

₹10,50,000

₹10,00,000

₹10,05,000

✅ Correct Option: 4

The problem requires finding the present value needed to withdraw ₹5000 at the beginning of every month forever, with 6% annual interest compounded monthly.

The annual interest rate is 6%, compounded monthly.

Monthly interest rate:

$i = \frac{6\%}{12}$

$i = 0.5\%$

$i = 0.005$

Since payments are received at the beginning of each month and continue forever, this is a perpetuity due.

The present value formula for a perpetuity due is:

$PV = \text{Payment} \times \frac{(1 + i)}{i}$

where Payment = ₹5000 and $i = 0.005$

Substituting the values:

$PV = 5000 \times \frac{(1 + 0.005)}{0.005}$

$PV = 5000 \times \frac{1.005}{0.005}$

$PV = 5000 \times 201$

$PV = 1005000$

Therefore, the sum needed to invest now is ₹10,05,000.

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At what rate of interest will the present value of a perpetuity of Rs. 1000 payable at the end of every six months be Rs. 40000?

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Mrs. Soma takes a loan of ₹ 5,00,000 with 10% annual interest rate for 5 years. What will be her EMI under flat rate system?

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?

Solution

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