To solve this problem, we can use the compound interest formula: A = P (1 + r/n) nt, where A is the future value, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.
(i) To find the compound interest after one year, we need to plug in the values given in the problem: P = 10,000, r = 0.10, n = 1, and t = 1. Then we get:
A = 10,000 (1 + 0.10/1) 1*1 A = 10,000 (1.10) A = 11,000
The future value after one year is 11,000. To find the compound interest, we subtract the principal amount from the future value:
Compound interest = A - P Compound interest = 11,000 - 10,000 Compound interest = 1,000
The compound interest after one year is 1,000.
(ii) To find the compound interest for two years, we need to change the value of t to 2 in the formula:
A = 10,000 (1 + 0.10/1) 1*2 A = 10,000 (1.10)^2 A = 12,100
The future value after two years is 12,100. To find the compound interest, we subtract the principal amount from the future value:
Compound interest = A - P Compound interest = 12,100 - 10,000 Compound interest = 2,100
The compound interest for two years is 2,100.
(iii) To find the sum of money required to clear the debt at the end of two years, we simply use the future value that we calculated in part (ii):
Sum of money required = A Sum of money required = 12,100
The sum of money required to clear the debt at the end of two years is 12,100.
(iv) To find the difference between the compound interest and the simple interest at the same rate for two years, we need to calculate the simple interest first. The formula for simple interest is: I = Prt, where I is the simple interest, P is the principal amount, r is the annual interest rate, and t is the number of years.
Using the values given in the problem: P = 10,000, r = 0.10, and t = 2, we get:
I = Prt I = 10,000 * 0.10 * 2 I = 2,000
The simple interest for two years is 2,000. To find the difference between the compound interest and the simple interest, we subtract them:
Difference = Compound interest - Simple interest Difference = 2,100 - 2,000 Difference = 100
The difference between the compound interest and the simple interest at the same rate for two years is 100.