Question

In an R.D., the maturity value is the sum of the total amount deposited and the interest. It P is the amount deposited every month for n months and R is the rate of interest, then interest I is equal to ______.

विकल्प

• `P xx n/12 xx R/100`

• `P xx (n(n - 1))/12 xx R/100`

• `P xx (n(n + 1))/(2 xx 12) xx R/100`

• `P xx n/(2 xx 12) xx R/100`

Answer 1

In an R.D., the maturity value is the sum of the total amount deposited and the interest. It P is the amount deposited every month for n months and R is the rate of interest, then interest I is equal to `underlinebb(P xx (n(n + 1))/(2 xx 12) xx R/100)`.

Explanation:

Each monthly instalment P earns simple interest for a different number of months: 1, 2, ..., n.

The total “interest-months” = `1 + 2  + ... + n = (n(n + 1))/2`. 

So, `I = P xx R/100 xx ("Total months")/12` 

= `P xx R/100 xx [(n(n + 1))/2] xx 1/12` 

= `P xx (n(n + 1))/(2 xx 12) xx R/100`