How much will $3000 amount to after 4 years at a compound interest rate of 7% pe

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Question: How much will $3000 amount to after 4 years at a compound interest rate of 7% per annum?

Options:

Correct Answer: $4000.00

Solution:

Amount = P(1 + r/n)^(nt) = 3000(1 + 0.07/1)^(1*4) = 3000(1.3107961) = 3932.39

How much will $3000 amount to after 4 years at a compound interest rate of 7% per annum?

How much will $3000 amount to after 4 years at a compound interest rate of 7% per annum?

Step 1: Identify the principal amount (P), which is $3000.
Step 2: Identify the annual interest rate (r), which is 7% or 0.07 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 4 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 + 0.07/1)^(1*4).
Step 7: Simplify the expression inside the parentheses: 1 + 0.07 = 1.07.
Step 8: Calculate the exponent: 1 * 4 = 4.
Step 9: Now the formula looks like this: Amount = 3000(1.07)^4.
Step 10: Calculate (1.07)^4, which is approximately 1.3107961.
Step 11: Multiply this result by the principal amount: 3000 * 1.3107961.
Step 12: The final amount is approximately $3932.39.

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.