Question

Si una empresa obtiene un préstamo de S/3000 a seis años de plazo, con una tasa de interés compuesto del 15 % anual capitalizable semestralmente, ¿qué monto debe pagar en la fecha de vencimiento y qué interés?

Answer 1

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.