If $1500 is invested at an interest rate of 4% compounded annually, what will be

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Question: If $1500 is invested at an interest rate of 4% compounded annually, what will be the total amount after 5 years?

Options:

Correct Answer: $1833.00

Solution:

Total Amount = P(1 + r/n)^(nt) = 1500(1 + 0.04/1)^(1*5) = 1500(1.2166529) = 1824.98

If $1500 is invested at an interest rate of 4% compounded annually, what will be the total amount after 5 years?

If $1500 is invested at an interest rate of 4% compounded annually, what will be the total amount after 5 years?

Correct Answer: 1824.98

Step 1: Identify the principal amount (P), which is the initial investment. Here, P = 1500.
Step 2: Identify the annual interest rate (r). Here, r = 4%, which can be written as a decimal: 0.04.
Step 3: Identify the number of times the interest is compounded per year (n). Since it is compounded annually, n = 1.
Step 4: Identify the number of years the money is invested (t). Here, t = 5 years.
Step 5: Use the formula for compound interest: Total Amount = P(1 + r/n)^(nt).
Step 6: Substitute the values into the formula: Total Amount = 1500(1 + 0.04/1)^(1*5).
Step 7: Simplify the expression inside the parentheses: 1 + 0.04 = 1.04.
Step 8: Calculate the exponent: 1 * 5 = 5, so we have (1.04)^5.
Step 9: Calculate (1.04)^5, which is approximately 1.2166529.
Step 10: Multiply this result by the principal amount: 1500 * 1.2166529 = 1824.98.
Step 11: The total amount after 5 years is approximately $1824.98.

Compound Interest – The calculation of interest where the interest earned over time is added to the principal, leading to interest being earned on interest.
Formula Application – Using the compound interest formula A = P(1 + r/n)^(nt) to calculate the total amount after a specified time.
Understanding Variables – Identifying and correctly substituting the principal (P), rate (r), number of times interest is compounded per year (n), and time in years (t).