nu gives Rs. 2,50,000 to Bhim at 12% p.a. compound interest for two years. Bhim gives 80% of the money received from Anu to Chinu at 20% p.a. interest, compounded half yearly for two years. Two years hence when he receives his due amount from Chinu, Bhim gives Anu her due amount. What is the amount (in Rs.) left with Bhim?1) 29,2202) 28,4403) 29,8404) 22,780
Question
nu gives Rs. 2,50,000 to Bhim at 12% p.a. compound interest for two years. Bhim gives 80% of the money received from Anu to Chinu at 20% p.a. interest, compounded half yearly for two years. Two years hence when he receives his due amount from Chinu, Bhim gives Anu her due amount. What is the amount (in Rs.) left with Bhim?1) 29,2202) 28,4403) 29,8404) 22,780
Solution
To solve this problem, we need to calculate the compound interest for both transactions and then subtract the amount Bhim owes Anu from the amount he receives from Chinu.
Step 1: Calculate the amount Bhim owes Anu. The formula for compound interest is A = P(1 + r/n)^(nt), where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (in decimal).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested for in years.
For Anu's loan to Bhim, P = Rs. 2,50,000, r = 12% or 0.12, n = 1 (compounded annually), and t = 2 years.
So, A = 2,50,000(1 + 0.12/1)^(1*2) = Rs. 3,15,600.
Step 2: Calculate the amount Chinu owes Bhim. Bhim gives 80% of the money received from Anu to Chinu, so P = 80% of Rs. 2,50,000 = Rs. 2,00,000. The interest rate is 20% or 0.20, and it's compounded half yearly, so n = 2, and t = 2 years.
So, A = 2,00,000(1 + 0.20/2)^(2*2) = Rs. 2,94,400.
Step 3: Subtract the amount Bhim owes Anu from the amount he receives from Chinu. The amount left with Bhim = Amount received from Chinu - Amount owed to Anu = Rs. 2,94,400 - Rs. 3,15,600 = -Rs. 21,200.
This means Bhim doesn't have any money left and still owes Rs. 21,200. So, none of the options given are correct.
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