Question

Use the compound interest formulas A =P( 1+r/n) ⁿᵗ and A = Pe ʳᵗto solve the problem given. Round answers to the nearest cent.

Find the accumulated value of an investment of $25,000 for 3 years at an interest rate of 5% if the money is
a. compounded semiannually;
b. compounded quarterly,
c. compounded monthly
d. compounded continuously.
a. What is the accumulated value if the money is compounded semiannually?

Answer 1

The accumulated value of a $25,000 investment at a 5% interest rate compounded semiannually for 3 years is $28,992.20, when rounded to the nearest cent.

Step-by-step explanation:

To find the accumulated value of an investment of $25,000 for 3 years at an interest rate of 5% when the money is compounded semiannually, you can use the compound interest formula:

A = P(1 + r/n)^(nt)

Where:

• P is the principal amount ($25,000)
• r is the annual interest rate (5% or 0.05)
• n is the number of times the interest is compounded per year (2 for semiannual)
• t is the number of years the money is invested (3)

Substituting these values into the formula, we get:

A = 25000(1 + 0.05/2)^(2*3)

A = 25000(1 + 0.025)^(6)

A = 25000(1.025)^(6)

A = 25000(1.159688)

A = $28,992.20

Thus, the accumulated value after 3 years when compounded semiannually is $28,992.20, rounded to the nearest cent.