A person invests $1000 at a compound interest rate of 5% per annum. What will be

₹0.0

Question: A person invests $1000 at a compound interest rate of 5% per annum. What will be the amount after 2 years?

Options:

Correct Answer: $1100.25

Solution:

Amount = P(1 + r/n)^(nt) = 1000(1 + 0.05/1)^(1*2) = 1000(1.05)^2 = 1102.5.

A person invests $1000 at a compound interest rate of 5% per annum. What will be the amount after 2 years?

A person invests $1000 at a compound interest rate of 5% per annum. What will be the amount after 2 years?

Step 1: Identify the principal amount (P), which is $1000.
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 (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 = 1000(1 + 0.05/1)^(1*2).
Step 7: Simplify the expression inside the parentheses: Amount = 1000(1 + 0.05)^(2).
Step 8: Calculate the value inside the parentheses: Amount = 1000(1.05)^(2).
Step 9: Calculate (1.05)^2, which equals 1.1025.
Step 10: Multiply by the principal amount: Amount = 1000 * 1.1025.
Step 11: The final amount after 2 years is $1102.50.

Compound Interest – Understanding how compound interest works, including the formula and its components (principal, rate, time, and compounding frequency).
Exponents – Applying exponent rules to calculate the growth of the investment over time.