If $1200 is invested at a compound interest rate of 7% per annum, what will be t

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Question: If $1200 is invested at a compound interest rate of 7% per annum, what will be the total amount after 5 years?

Options:

Correct Answer: $1685.06

Solution:

Amount = P(1 + r/n)^(nt) = 1200(1 + 0.07/1)^(1*5) = 1200(1.402552) = 1685.06

If $1200 is invested at a compound interest rate of 7% per annum, what will be the total amount after 5 years?

If $1200 is invested at a compound interest rate of 7% per annum, what will be the total amount after 5 years?

Step 1: Identify the principal amount (P), which is $1200.
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 the money is invested (t), which is 5 years.
Step 5: Use the compound interest formula: Amount = P(1 + r/n)^(nt).
Step 6: Substitute the values into the formula: Amount = 1200(1 + 0.07/1)^(1*5).
Step 7: Simplify the expression inside the parentheses: 1 + 0.07 = 1.07.
Step 8: Calculate the exponent: 1*5 = 5.
Step 9: Now the formula looks like this: Amount = 1200(1.07)^5.
Step 10: Calculate (1.07)^5, which is approximately 1.402552.
Step 11: Multiply this result by the principal: Amount = 1200 * 1.402552.
Step 12: Calculate the final amount: 1200 * 1.402552 = 1685.06.

Compound Interest – The process of earning interest on both the initial principal and the accumulated interest from previous periods.
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 values for principal (P), rate (r), number of times interest applied per time period (n), and time (t).