A dealer bought painting for N500 and 2 years later sold it for N650 in reckoning his rate of profit he takes into consideration the fact that his money could have been interested for this time at 4% compound interest. Find his true rate of profit.?

All_for_one

2 years ago

To find the dealer's true rate of profit, we need to consider the opportunity cost of the money that he invested in the painting for 2 years. He could have earned interest on that money at a 4% compound interest rate. Let's break down the calculation step by step.

1. Calculate the future value of the initial investment at a 4% compound interest rate for 2 years.

FV = PV x (1 + r)^n

Where:
PV = Present value (initial investment)
r = Interest rate per period (4% or 0.04 as a decimal)
n = Number of periods (2 years)

FV = N500 x (1 + 0.04)^2
FV = N500 x (1.04)^2
FV = N500 x 1.0816
FV ≈ N540.80

So, if the dealer had not invested in the painting and instead put N500 in a 4% compound interest account for 2 years, he would have approximately N540.80.

2. Now, let's calculate the dealer's actual profit:
Profit = Selling Price - Initial Investment
Profit = N650 - N500
Profit = N150

3. To find the true rate of profit, we need to compare the profit to the opportunity cost (what he could have earned in interest):

True Rate of Profit = (Profit / Opportunity Cost) x 100%
True Rate of Profit = (N150 / N540.80) x 100%
True Rate of Profit ≈ 27.74%

So, the dealer's true rate of profit is approximately 27.74%. This accounts for the fact that he could have earned interest on his money during the 2 years he held the painting.

Faheemadeiza2012

2 years ago

To find the dealer's true rate of profit, we need to calculate the compound interest that his money could have earned in 2 years at a rate of 4%. The formula for compound interest is: A = P(1 + r/n)^(nt) Where: A = the final amount P = the principal amount (initial investment) r = annual interest rate (as a decimal) n = number of times that interest is compounded per year t = number of years Let's plug in the values: P = N500 r = 4% = 0.04 n = 1 (since we are compounding annually) t = 2 A = 500(1 + 0.04/1)^(1*2) A = 500(1 + 0.04)^2 A = 500(1.04)^2 A = 500(1.0816) A = 540.80 The compound interest earned in 2 years at 4% is N540.80. Now let's calculate the dealer's true rate of profit: True Rate of Profit = (Selling Price - Cost Price) / Cost Price * 100 Selling Price = N650 Cost Price = N500 True Rate of Profit = (650 - 500) / 500 * 100 True Rate of Profit = 150 / 500 * 100 True Rate of Profit = 30% Therefore, the dealer's true rate of profit is 30%.