Banking (Recurring Deposit Accounts)

In a recurring deposit you pay the same amount every month, but the bank does not pay interest on all of it for the full time. The first installment stays in the account for all n months, the second for (n minus 1) months, the third for (n minus 2) months, and the last installment stays for just 1 month. So you cannot simply use total money times time. Instead you add up the months: n plus (n minus 1) plus ... plus 1, which equals n(n+1)/2. That single trick turns many separate interest sums into one neat calculation.

Because each installment is the same amount P, the bank treats the whole account as if a principal of P had been deposited for n(n+1)/2 months. That is why the interest formula is I = P times n(n+1)/2 times rate/100 times 1/12. The 1/12 appears because the rate is per annum but the time is counted in months, so each month is 1/12 of a year. This is plain simple interest, just applied to a clever combined time.

Once you have the interest I, the maturity value is easy: it is everything you put in plus the interest the bank adds. The total you deposited is P times n. So the maturity value MV = P times n plus I. In exam problems you may be given the maturity value and asked to find the monthly installment, the rate, or the time. The method is always the same: write down what you know, substitute into the two formulas, and solve the resulting equation step by step.

Class 10 board questions test whether you keep your quantities straight. Always note the monthly installment P, the number of months n (convert years to months by multiplying by 12), and the rate per annum. A common trap is using time in years inside the formula; the time must be in months because of the 1/12 factor. Another trap is forgetting that the maturity value includes the deposits, not just the interest. Label every value with its unit and the rest is careful arithmetic.