Mr.Zia borrows rs .25,000today with interest at 12%compounded annually .he agrees to pay rs.20,000 two years from today and the balance three years from today.find the amount of the final payment?
To find the amount of the final payment, we need to calculate the future value of the loan after three years.
First, let's calculate the future value of the loan after two years. We can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = The future value of the loan
P = The principal amount (initial loan amount)
r = Annual interest rate (in decimal form)
n = Number of times interest is compounded per year
t = Number of years
Given:
P = Rs. 25,000
r = 12% (0.12 in decimal form)
n = 1 (compounded annually)
t = 2 years
Using the formula, we have:
A = 25,000(1 + 0.12/1)^(1*2)
A = 25,000(1 + 0.12)^2
A = 25,000(1.12)^2
A ≈ 25,000(1.2544)
A ≈ Rs. 31,360
Therefore, after two years, the value of the loan will be approximately Rs. 31,360.
Now, let's calculate the final payment after three years. We will use the same formula, but this time the principal amount (P) will be Rs. 31,360.
Given:
P = Rs. 31,360
r = 12% (0.12 in decimal form)
n = 1 (compounded annually)
t = 3 years
Using the formula, we have:
A = 31,360(1 + 0.12/1)^(1*3)
A = 31,360(1 + 0.12)^3
A = 31,360(1.12)^3
A ≈ 31,360(1.404928)
A ≈ Rs. 44,072.59 (rounded to two decimal places)
Therefore, the amount of the final payment will be approximately Rs. 44,072.59.
To find the amount of the final payment, we need to calculate the total amount to be paid by Mr. Zia three years from today. Here's how you can calculate it:
Step 1: Calculate the interest earned on the borrowed amount after two years.
We can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = Total amount after interest
P = Principal amount (borrowed) = Rs. 25,000
r = Annual interest rate (as a decimal) = 12% = 0.12
n = Number of times interest is compounded per year = 1 (annually)
t = Number of years = 2
Plugging these values into the formula:
A = 25000(1 + 0.12/1)^(1*2)
A = 25000(1 + 0.12)^2
A ≈ 25000(1.12)^2
A ≈ 25000(1.2544)
A ≈ Rs. 31,360
Step 2: Calculate the final payment amount after three years.
To find the final payment, we deduct the amount already paid (Rs. 20,000) from the total amount after three years.
Final Payment = Total amount after three years - Amount already paid = Rs. 31,360 - Rs. 20,000
Final Payment ≈ Rs. 11,360
Therefore, the amount of the final payment will be approximately Rs. 11,360.