Sneha opened a cumulative time deposit account with a bank...

Sneha opened a cumulative time deposit account with a bank and deposits Rs 500 per month for $1 \frac{1}{4}$ years. If she receives $\mathrm{Rs} 300$ as interest, find the rate of interest per annum.
(1) $6 \%$
(2) $8 \%$
(3) $7.5 \%$
(4) $10 \%$

Key Concepts

Interest Rate per Annum

The interest rate per annum is the annual rate at which interest is applied to the deposited funds. In problems involving periodic deposits, it is necessary to relate the total accumulated interest to the average or weighted sum of the deposit durations in order to solve for the annual rate, ensuring that the calculated rate properly reflects the effective interest accumulated over the period.

Weighted Interest Accumulation

In scenarios where deposits are made periodically, each deposit accrues interest for a different length of time. The overall interest earned is the sum of the interests on each individual deposit, weighted by the duration each deposit remains invested. This concept is crucial for calculating the effective interest rate when contributions occur at regular intervals.

Cumulative (Recurring) Deposit Calculation

A cumulative or recurring deposit involves making regular contributions over a period of time. Each deposited amount earns interest for a period corresponding to the time it remains in the account, which requires setting up a system that accounts for these staggered time intervals when computing the total interest earned.

Time Value of Money

This concept refers to the idea that money available now is worth more than the same amount in the future due to its potential earning capacity. In problems involving deposits and interest, this principle requires proper accounting of the timing of cash flows, as money deposited earlier earns interest for a longer period than money deposited later.

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