Question

The money needed to invest now, so as to get ₹7500 at the beginning of each month forever (starting from the current month) if the money is worth 9% per annuum compounded monthly is.

• A. ₹10.05,000
• B. ₹9.05,000
• C. ₹10,07,500
• D. ₹9.50,000

Answer 1

The Correct Option is C

The problem requires calculating the present value of a perpetuity, which provides a fixed amount of money forever. Here, the perpetuity pays ₹7500 at the beginning of each month. Since the payments start immediately, we deal with an annuity due.

To calculate the present value of an annuity due, we adjust the formula for a regular perpetuity. The formula for the present value \(PV\) of a perpetuity paying \(R\) per period at an interest rate \(i\) per period is:

\(PV_{\text{regular}}=\frac{R}{i}\)

Given that the interest rate is 9% per annum compounded monthly, we first convert it to a monthly rate:

\(i_{\text{monthly}}=\frac{9\%}{12}=0.75\%\)

Converting to a decimal gives:

\(i_{\text{monthly}}=\frac{0.75}{100}=0.0075\)

Now adjusting for an annuity due (payments at the beginning of the period), the present value is given by:

\(PV_{\text{due}}=PV_{\text{regular}}\times(1+i)=\frac{R}{i}\times(1+i)\)

Substituting the values:

\(PV_{\text{due}}=\frac{7500}{0.0075}\times(1+0.0075)\)

First, compute the regular perpetuity:

\(PV_{\text{regular}}=7500/0.0075=1000000\)

Then apply the annuity due adjustment:

\(PV_{\text{due}}=1000000\times1.0075=1007500\)

Thus, the amount needed to invest now is ₹10,07,500.

The correct answer is ₹10,07,500.