Statistics & Applications

Financial Math

Medium

applied

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?

Rs 10,05,000

Rs 15,00,000

Rs 10,50,000

Rs 12,50,000

✅ Correct Option: 1

The goal is to invest a lump sum today to withdraw Rs. 5000 at the beginning of every month, forever. The interest rate is 6% per annum compounded monthly.

Since money is withdrawn at the beginning of each month (not the end), this is a perpetuity due.

The annual interest rate is 6%, compounded monthly.

Monthly Interest Rate (r) = Annual Rate ÷ 12

$r = 6\% ÷ 12$

$r = 0.5\%$ per month

In decimal form: $r = 0.005$

For payments at the beginning of each period that continue forever, the present value formula is:

$\text{Present Value} = \frac{\text{Payment} \times (1 + r)}{r}$

The $(1 + r)$ factor adjusts for the first payment happening immediately at month 0.

Payment = Rs. 5000

$r = 0.005$

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

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

$\text{PV} = \frac{5025}{0.005}$

$\text{PV} = 5025 \times 200$

$\text{PV} = 10,05,000$

Therefore, the sum of money needed to invest now is Rs. 10,05,000.

2026: 21 May Shift 2

Geetansh invested ₹27,000 and it grows to ₹81,000 in 2 years. The CAGR % will be:

2025: 21 May Shift 1

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?

2025: 27 May Shift 1

If an asset costs Rs. 50,000 with an estimated useful life of 6 years and a scrap value of Rs. 5000. Then by using a linear depreciation method, the annual depreciation of the asset will be:

2026: 26 May Shift 2

Chintan has borrowed ₹ 5,00,000 from a bank to purchase a car and decided to repay the loan in equal monthly installments in 10 years. If bank charges interest at 6% per annum compounded monthly, the EMI on reducing balance method will be : (Given $(1.005)^{120} = 1.82$ )

2026: 19 May Shift 1

A person has set up a sinking fund in order to have ₹ 20,000 in 10 years for his children's education. The amount to set aside each quarter into an account paying 6% per annum compounded quarterly is: [use $(1.015)^{40} = 1.8140$ ]

2025: 21 May Shift 2

A money lender charges Rs10 for Rs100 per month in advance then effective rate of interest per annum charged by money lender is: [given $\left(\frac{10}{9}\right)^{12} \approx 3.541$ ]

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?

Solution

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