If $2500 is invested at a compound interest rate of 5% per annum, what will be t

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Question: If $2500 is invested at a compound interest rate of 5% per annum, what will be the total amount after 4 years?

Options:

Correct Answer: $3031.25

Solution:

Amount = P(1 + r/n)^(nt) = 2500(1 + 0.05/1)^(1*4) = 2500(1.215506) = 3031.25

If $2500 is invested at a compound interest rate of 5% per annum, what will be the total amount after 4 years?

If $2500 is invested at a compound interest rate of 5% per annum, what will be the total amount after 4 years?

Step 1: Identify the principal amount (P), which is $2500.
Step 2: Identify the annual interest rate (r), which is 5% or 0.05 in decimal form.
Step 3: Identify the number of times interest is compounded per year (n), which is 1 for annual compounding.
Step 4: Identify the number of years the money is invested (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 = 2500(1 + 0.05/1)^(1*4).
Step 7: Simplify the expression inside the parentheses: 1 + 0.05 = 1.05.
Step 8: Calculate the exponent: 1 * 4 = 4.
Step 9: Now the formula looks like this: Amount = 2500(1.05)^4.
Step 10: Calculate (1.05)^4, which is approximately 1.215506.
Step 11: Multiply 2500 by 1.215506 to find the total amount: 2500 * 1.215506 = 3038.77.
Step 12: The total amount after 4 years is approximately $3038.77.

Compound Interest – The calculation of interest where the interest earned is added to the principal, and future interest calculations are based on the new total.
Formula Application – Using the compound interest formula A = P(1 + r/n)^(nt) to calculate the total amount after a certain period.
Understanding Variables – Identifying and correctly substituting the principal (P), rate (r), number of times interest applied per time period (n), and time (t) into the formula.