Find the rate percent if the banker’s gain on a certain sum due two and a half year hence is 1/5 of the banker’s discount

General
1

find the rate percent if the banker’s gain on a certain sum due two and a half year hence is 1/5 of the banker’s discount.

2

To find the rate percent when the banker’s gain on a certain sum due two and a half years hence is 1/5 of the banker’s discount, we need to understand the concepts of banker’s gain and discount.

Banker’s gain refers to the additional amount that a banker earns when lending money, usually calculated as a percentage of the principal amount.

Discount, on the other hand, is a deduction or reduction made from the original amount or value, often given as an incentive or to settle a transaction.

In this case, the given information states that the banker’s gain on a certain sum due in two and a half years is 1/5 of the banker’s discount. To calculate the rate percent, we can follow these steps:

  1. Let’s assume the original sum (principal) is P.
  2. The discount is calculated as the difference between the principal and the sum received after the discount. Let’s denote the discount as D.
  3. The gain is calculated as the difference between the principal and the sum received after the gain. Let’s denote the gain as G.

According to the given information, G = 1/5 * D.

To calculate the rate percent, we need to determine the time period involved in the transaction. Here, the sum is due in two and a half years, or 2.5 years.

Now, we can set up the formula for calculating the rate percent:

Rate percent = (G / P) * (100 / T)

where T is the time period in years.

Plugging in the values we have, G = 1/5 * D and T = 2.5 years, the formula becomes:

Rate percent = ((1/5) * D / P) * (100 / 2.5)

Simplifying further:

Rate percent = (1/10) * (D / P) * (100 / 2.5)

Rate percent = (1/10) * (D / P) * 40

Now, we need more information to proceed. We either need the value of the principal (P) or the discount (D) to calculate the rate percent accurately.