1. Find the amount and the compound interest on rs.12800 for 1 year at 15/2%p.a. Componded semi-annually.
2.find the amount and the compound interest on rs.24000 for 6 months if the interest is payable quarterly at the rate of 20 paise a rupee per annum.
13778
Amount 14792 compound interest 1992
You are bad mathematician you are matharchod
To find the compound interest and amount in these scenarios, we'll first calculate the semi-annual and quarterly interest rates respectively, and then use the compound interest formula:
Compound Interest Formula:
A = P(1 + r/n)^(nt) - P
Where:
A = Amount
P = Principal amount
r = Annual interest rate
n = Number of times interest is compounded per year
t = Time in years
Let's calculate for each scenario:
1. Find the amount and compound interest on Rs. 12,800 for 1 year at 15/2% p.a., compounded semi-annually.
Step 1: Convert the interest rate to a decimal.
15/2% = 15/2 / 100 = 0.075
Step 2: Calculate the semi-annual interest rate.
Semi-annual rate = 0.075 / 2 = 0.0375
Step 3: Apply the compound interest formula.
P = Rs. 12,800
n = 2 (compounded semi-annually)
t = 1 (1 year)
A = 12800(1 + 0.0375/2)^(2*1) - 12800
A = 12800(1 + 0.01875)^2 - 12800
A ≈ 12800(1.01875)^2 - 12800
A ≈ 12800(1.038207) - 12800
A ≈ 13278.856 - 12800
A ≈ Rs. 478.856
The amount after 1 year will be approximately Rs. 13,278.856, and the compound interest will be approximately Rs. 478.856.
2. Find the amount and compound interest on Rs. 24,000 for 6 months if the interest is payable quarterly at the rate of 20 paise per rupee per annum.
Step 1: Convert the interest rate to a decimal.
20 paise = 20/100 = 0.2
Step 2: Calculate the quarterly interest rate.
Quarterly rate = 0.2 / 4 = 0.05
Step 3: Apply the compound interest formula.
P = Rs. 24,000
n = 4 (compounded quarterly)
t = 6 months = 6/12 = 0.5 years
A = 24000(1 + 0.05/4)^(4*0.5) - 24000
A = 24000(1 + 0.0125)^2 - 24000
A ≈ 24000(1.0125)^2 - 24000
A ≈ 24000(1.025) - 24000
A ≈ 24600 - 24000
A ≈ Rs. 600
The amount after 6 months will be Rs. 24,600, and the compound interest will be Rs. 600.