Final answer:
To calculate the total amount due and the interest incurred on a S/3000 loan at a 15% annual compound interest rate capitalized semiannually for six years, use the compound interest formula and then subtract the principal to find the interest.
Step-by-step explanation:
If a company obtains a loan of S/3000 for a term of six years, with a compound interest rate of 15% per annum that is capitalized semiannually, we can calculate the total amount that must be paid at maturity and the total interest incurred using the compound interest formula:
A = P(1 + \frac{r}{n})^{nt}
Where:
A is the amount of money accumulated after n years, including interest.
P is the principal amount (the initial amount of money).
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 for, in years.
In this case:
P = S/3000
r = 0.15 (15% expressed as a decimal)
n = 2 (since the interest is compounded semiannually)
t = 6 years
Plugging the values into the formula, we get:
A = 3000(1 + \frac{0.15}{2})^{2 \times 6} = 3000(1 + 0.075)^{12}
After calculating the value in the parentheses and raising it to the 12th power, we would get the total amount A that needs to be paid at maturity. To find out the interest incurred, we subtract the principal from this amount:
Interest = A - P
Remember to use a calculator to compute the exact values and to follow the order of operations properly.