Question

$5000 is invested in an account earning 9% interest compounded semi-annually for 10 years. Show the substitution into the equation A = P(1 + r/n)^(nt), then determine the total amount for the investment.

A. A = 5000(1 + 0.045)^(210)
B. A = 5000(1 + 0.09)^(210)
C. A = 5000(1 + 0.045/2)^(210)
D. A = 5000(1 + 0.09/2)^(210)

Answer 1

The total amount for the investment can be found by substituting into the compound interest formula with the given values, leading to the correct substitution as A = 5000(1 + 0.09/2)^(2*10), which means option D is correct.

Step-by-step explanation:

To determine the total amount for the investment, we need to substitute the values into the compound interest formula: A = P(1 + r/n)^(nt), where:

• P is the principal amount ($5000),
• r is the annual interest rate (9% or 0.09),
• n is the number of times interest is compounded per year (2 for semi-annual),
• t is the number of years (10).

The correct substitution, therefore, is:

A = 5000(1 + 0.09/2)^(2*10)

Let's break it down:

1. The interest rate per period, r/n, is 0.09/2.
2. The number of periods, nt, is 2 * 10.

Substituting these values into the formula, we get:

A = 5000(1 + 0.045)^(20)

Thus, option D is correct.