Final answer:
To calculate the principal of a compound interest loan when you know the total amount paid, the interest rate, and the time, use the compound interest formula A = P(1 + r/n)^(nt) and solve for P. With an amount of $16,000, a 7% interest rate compounded semi-annually over 5 years, you can find the original loan amount, also known as the principal.Therefore, the correct answer is option A, perpendicular to the path.
Step-by-step explanation:
To find the principal of a loan when the total amount paid and the interest rate are known, we need to use the formula for compound interest. The question states that the total amount paid on a 5-year loan was $16,000, with an interest rate of 7% compounded semi-annually, and we are tasked with finding the original principal amount.
The compound interest formula is:
A = P(1 + r/n)^(nt)
Where:
- A is the future value of the investment/loan, including interest.
- P is the principal amount.
- r is the annual interest rate (decimal).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested or borrowed for, in years.
Given A = $16,000, r = 7% or 0.07, n = 2 (since interest is compounded semi-annually), and t = 5, we can calculate the principal P.
P = A / (1 + r/n)^(nt)
Substitute the given values into the formula:
P = $16,000 / (1 + 0.07/2)^(2*5)
Solving for P gives us the principal of the loan.
Understanding compound interest is crucial as it is the calculation of interest on both the initial principal and the accumulated interest from previous periods. It can make a significant difference in the total amount of money accrued over time compared to simple interest, which only calculates interest on the principal amount.
Therefore, the correct answer is not mention.