If $1500 is invested at a compound interest rate of 4% per annum, how much will

If $1500 is invested at a compound interest rate of 4% per annum, how much will it amount to after 2 years?

If $1500 is invested at a compound interest rate of 4% per annum, how much will it amount to after 2 years?

Step 1: Identify the principal amount (P), which is $1500.
Step 2: Identify the annual interest rate (r), which is 4% or 0.04 in decimal form.
Step 3: Identify the number of times interest is compounded per year (n). Since it is compounded annually, n = 1.
Step 4: Identify the number of years (t) the money is invested, which is 2 years.
Step 5: Use the compound interest formula: Amount = P(1 + r/n)^(nt).
Step 6: Substitute the values into the formula: Amount = 1500(1 + 0.04/1)^(1*2).
Step 7: Simplify the expression inside the parentheses: 1 + 0.04 = 1.04.
Step 8: Calculate the exponent: 1 * 2 = 2, so we have (1.04)^2.
Step 9: Calculate (1.04)^2, which equals 1.0816.
Step 10: Multiply this result by the principal: Amount = 1500 * 1.0816.
Step 11: Calculate the final amount: 1500 * 1.0816 = 1624.00.

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).
Interest Rate Conversion – Converting the annual interest rate into a decimal for calculations.
Time Period Calculation – Determining the total time the money is invested or borrowed, in years.