How much will $3000 grow to after 6 years at a compound interest rate of 9% per

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Question: How much will $3000 grow to after 6 years at a compound interest rate of 9% per annum?

Options:

Correct Answer: $4503.00

Solution:

Amount = P(1 + r/n)^(nt) = 3000(1 + 0.09/1)^(1*6) = 3000(1.677100) = 5003.00

How much will $3000 grow to after 6 years at a compound interest rate of 9% per annum?

How much will $3000 grow to after 6 years at a compound interest rate of 9% per annum?

Step 1: Identify the principal amount (P), which is $3000.
Step 2: Identify the annual interest rate (r), which is 9% or 0.09 in decimal form.
Step 3: Identify the number of times interest is compounded per year (n). Since it's compounded annually, n = 1.
Step 4: Identify the number of years (t), which is 6 years.
Step 5: Use the compound interest formula: Amount = P(1 + r/n)^(nt).
Step 6: Substitute the values into the formula: Amount = 3000(1 + 0.09/1)^(1*6).
Step 7: Simplify the expression inside the parentheses: 1 + 0.09 = 1.09.
Step 8: Calculate the exponent: 1 * 6 = 6.
Step 9: Now the formula looks like this: Amount = 3000(1.09)^6.
Step 10: Calculate (1.09)^6, which is approximately 1.677100.
Step 11: Multiply this result by the principal: Amount = 3000 * 1.677100.
Step 12: Calculate the final amount: 3000 * 1.677100 = 5003.00.

Compound Interest – The process of earning interest on both the initial principal and the accumulated interest from previous periods.
Formula Application – Understanding and correctly applying the compound interest formula: A = P(1 + r/n)^(nt).
Time Value of Money – The principle that money available now is worth more than the same amount in the future due to its potential earning capacity.