A sum of money invested at compound interest grows to $5000 in 3 years. If the rate of interest is 5% per annum, what was the principal amount?
Practice Questions
1 question
Q1
A sum of money invested at compound interest grows to $5000 in 3 years. If the rate of interest is 5% per annum, what was the principal amount?
$4320
$4500
$4800
$4900
Using A = P(1 + r)^n, we have 5000 = P(1 + 0.05)^3. Solving gives P ≈ $4320.
Questions & Step-by-step Solutions
1 item
Q
Q: A sum of money invested at compound interest grows to $5000 in 3 years. If the rate of interest is 5% per annum, what was the principal amount?
Solution: Using A = P(1 + r)^n, we have 5000 = P(1 + 0.05)^3. Solving gives P ≈ $4320.
Steps: 8
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 interest rate, and n is the number of years.
Step 3: Substitute the known values into the formula. Here, A = 5000, r = 0.05 (which is 5% as a decimal), and n = 3.
Step 4: The equation now looks like this: 5000 = P(1 + 0.05)^3.
Step 5: Calculate (1 + 0.05)^3. This equals (1.05)^3, which is approximately 1.157625.
Step 6: Now the equation is 5000 = P * 1.157625.
Step 7: To find P, divide both sides of the equation by 1.157625: P = 5000 / 1.157625.
Step 8: Calculate the value of P, which is approximately 4320.
