14.1k views
5 votes
Use the compound interest formulas A = P(1 + r/n)ⁿᵗ and A = Peʳᵗ to solve the problem given. Round answers to the nearest cent. Find the accumulated value of an investment of $20,000 for 6 years at an interest rate of 7% if the money is compounded semiannually.

A. $29,215.68

B. $29,624.51

C. $30,041.99

D. $30,468.32

User Supermitch
by
7.8k points

1 Answer

1 vote

Final answer:

Using the compound interest formula with the given values for principal amount, interest rate, compounding frequency, and time, the accumulated value of a $20,000 investment after 6 years at a 7% interest rate compounded semiannually is approximately $30,468.32.

Step-by-step explanation:

The problem asks us to find the accumulated value of an investment of $20,000 for 6 years at an interest rate of 7% compounded semiannually. To solve this, we can use the compound interest formula A = P(1 + r/n)^(nt), where:

  • P is the principal amount ($20,000)
  • r is the annual interest rate (0.07)
  • n is the number of times the interest is compounded per year (2)
  • t is the time the money is invested in years (6)

Plugging the values into the formula, we get:

A = 20000*(1 + 0.07/2)^(2*6)

A = 20000*(1 + 0.035)^(12)

A = 20000*(1.035)^12

Calculating using a calculator, we find:

A ≈ $30,468.32

Therefore, the accumulated value of the investment after 6 years is approximately $30,468.32, which corresponds to option D.

User Dafang Cao
by
8.3k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories