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Mathematics

₹ P is deposited for n number of months in a recurring deposit account which pays interest at the rate of r% per annum. The nature and time of interest calculated is :

  1. compound interest for n number of months

  2. simple interest for n number of months

  3. compound interest for one month

  4. simple interest for one month

Banking

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Answer

In a Recurring Deposit (RD), the interest is calculated using the concept of Equivalent Monthly Principal.

The first installment stays in the bank for nn months, the second for n - 1 months, and the last for 1 month. To simplify this, we use the sum of natural numbers formula to find the total "month-units" of interest:

Total monthly principal = P × n(n+1)2\dfrac{n(n + 1)}{2}

Because we have converted the entire duration into an equivalent principal for just one month, the time (T) used in the standard S.I. formula is :

T = 112\dfrac{1}{12} years

Final formula,

I = P×n(n+1)2×r100×112P \times \dfrac{n(n + 1)}{2} \times \dfrac{r}{100} \times \dfrac{1}{12}

The interest is simple in nature, and it is calculated on the equivalent principal for one month.

Hence, Option 4 is the correct option.

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