A sum of money invested at compound interest becomes $8000 in 5 years. If the ra

A sum of money invested at compound interest becomes $8000 in 5 years. If the rate of interest is 10% per annum, what was the principal amount?

A sum of money invested at compound interest becomes $8000 in 5 years. If the rate of interest is 10% per annum, what was the principal amount?

Step 1: Identify the formula for compound interest, which is A = P(1 + r)^n.
Step 2: In this formula, A is the amount of money after interest, P is the principal amount (the initial amount), r is the rate of interest, and n is the number of years.
Step 3: Substitute the known values into the formula. Here, A = 8000, r = 0.10 (which is 10% as a decimal), and n = 5.
Step 4: The equation now looks like this: 8000 = P(1 + 0.10)^5.
Step 5: Calculate (1 + 0.10)^5. This equals (1.10)^5, which is approximately 1.61051.
Step 6: Now the equation is 8000 = P * 1.61051.
Step 7: To find P, divide both sides of the equation by 1.61051: P = 8000 / 1.61051.
Step 8: Calculate the value of P, which is approximately 4965.45. Rounding gives P ≈ 5000.

Compound Interest – Understanding how compound interest works and how to apply the formula A = P(1 + r)^n to find the principal amount.