A certain amount of money is invested at a compound interest rate of 12% per ann

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What’s inside this PDF?

Question: A certain amount of money is invested at a compound interest rate of 12% per annum. If the amount becomes $5000 after 3 years, what was the principal?

Options:

$3500
$4000
$4500
$4800

Correct Answer: $4000

Solution:

Using A = P(1 + r)^t, we rearrange to find P = A / (1 + r)^t. Thus, P = 5000 / (1.12)^3 = $4000.

A certain amount of money is invested at a compound interest rate of 12% per ann

Practice Questions

A certain amount of money is invested at a compound interest rate of 12% per annum. If the amount becomes $5000 after 3 years, what was the principal?

$3500
$4000
$4500
$4800

Questions & Step-by-Step Solutions

A certain amount of money is invested at a compound interest rate of 12% per annum. If the amount becomes $5000 after 3 years, what was the principal?

Step 1: Identify the formula for compound interest, which is A = P(1 + r)^t.
Step 2: In this formula, A is the final amount, P is the principal (initial amount), r is the interest rate, and t is the time in years.
Step 3: We know that A = $5000, r = 12% (which is 0.12 as a decimal), and t = 3 years.
Step 4: Rearrange the formula to solve for P: P = A / (1 + r)^t.
Step 5: Substitute the known values into the rearranged formula: P = 5000 / (1 + 0.12)^3.
Step 6: Calculate (1 + 0.12) = 1.12.
Step 7: Raise 1.12 to the power of 3: (1.12)^3 = 1.404928.
Step 8: Now divide $5000 by 1.404928 to find P: P = 5000 / 1.404928.
Step 9: Calculate the final result: P ≈ $4000.

Compound Interest – Understanding how compound interest works and how to rearrange the formula to find the principal amount.
Exponential Growth – Recognizing that the investment grows exponentially over time due to compounding.
Rearranging Formulas – Ability to manipulate the compound interest formula to isolate the principal.

A certain amount of money is invested at a compound interest rate of 12% per ann

What’s inside this PDF?

A certain amount of money is invested at a compound interest rate of 12% per ann

Practice Questions

Questions & Step-by-Step Solutions

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