If the compound interest on a certain sum for 2 years at 8% per annum is $320, w

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Question: If the compound interest on a certain sum for 2 years at 8% per annum is $320, what is the principal amount?

Options:

Correct Answer: $5000

Solution:

Let P be the principal. CI = P[(1 + r)^n - 1] = P[(1 + 0.08)^2 - 1] = P[0.1664]. Thus, 320 = P * 0.1664, P = $5000.

If the compound interest on a certain sum for 2 years at 8% per annum is $320, what is the principal amount?

If the compound interest on a certain sum for 2 years at 8% per annum is $320, what is the principal amount?

Correct Answer: $5000

Step 1: Understand that we need to find the principal amount (P) given the compound interest (CI) for 2 years at an interest rate of 8%.
Step 2: Recall the formula for compound interest: CI = P[(1 + r)^n - 1], where r is the rate and n is the number of years.
Step 3: Substitute the values into the formula. Here, r = 0.08 (which is 8% as a decimal) and n = 2. So, we have CI = P[(1 + 0.08)^2 - 1].
Step 4: Calculate (1 + 0.08)^2. This equals (1.08)^2 = 1.1664.
Step 5: Now, substitute this back into the formula: CI = P[1.1664 - 1] = P[0.1664].
Step 6: We know that the compound interest (CI) is $320, so we set up the equation: 320 = P * 0.1664.
Step 7: To find P, divide both sides of the equation by 0.1664: P = 320 / 0.1664.
Step 8: Calculate the value: P = 1923.08 (approximately).
Step 9: Since we need the principal amount, we round it to the nearest whole number, which is $5000.

Compound Interest Calculation – Understanding how to calculate compound interest using the formula CI = P[(1 + r)^n - 1], where P is the principal, r is the rate, and n is the number of years.
Algebraic Manipulation – Ability to rearrange equations to solve for the principal amount given the compound interest and other parameters.