Statistics & Applications

Financial Math

Medium

applied

A trust invites a deposit of lumpsum amount from individual so that annual scholarship of Rs.5000 is paid. Rate of interest is 5% per annum. If the scholarship is to start at the end of this year then the amount needed to deposit to Trust is:

Rs. 60,000

Rs. 1,00,000

Rs. 1,25,000

Rs 1,50,000

✅ Correct Option: 2

The trust needs to pay Rs. 5,000 as scholarship every year, forever. The deposit will earn interest, and only the interest will be used to pay the scholarship. The original deposit remains untouched.

Annual scholarship required = Rs. 5,000

Interest rate = 5% per annum = $\frac{5}{100}$

For a perpetuity (payments that continue forever), the deposit amount is calculated as:

Deposit Amount = $\frac{\text{Annual Payment}}{\text{Interest Rate}}$

Deposit Amount = $\frac{5,000}{0.05}$

Deposit Amount = $5,000 \times 20$

Deposit Amount = Rs. 1,00,000

With Rs. 1,00,000 deposited:

Interest earned in one year = $1,00,000 \times \frac{5}{100}$

Interest earned in one year = Rs. 5,000

The interest earned exactly matches the annual scholarship requirement. The principal amount of Rs. 1,00,000 remains in the account to generate interest for subsequent years.

The amount needed to deposit is Rs. 1,00,000.

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Solution

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