Question

Type the correct answer in the box. round your answer to the nearest dollar. sarah plans to buy a car in five years, so she invests $10,000. she receives an annual interest rate of 5%, compounded semiannually. what’s the future value of the $10,000 investment in five years? the $10,000 investment is worth $ .

Answer 1

The future value of a $10,000 investment at a 5% annual interest rate, compounded semiannually for five years, is $12,801 after rounding to the nearest dollar.

Step-by-step explanation:

To calculate the future value of a $10,000 investment with a 5% annual interest rate compounded semiannually for five years, we need to use the compound interest formula:

FV = P × (1 + r/n)^(nt)

Where:

• FV is the future value of the investment,
• P is the principal amount ($10,000),
• r is the annual interest rate (5% or 0.05),
• n is the number of times interest is compounded per year (2 for semiannually),
• t is the number of years the money is invested (5 years).

First, divide the annual interest rate by the number of compounding periods per year:

r/n = 0.05/2 = 0.025

Next, add 1 to the result and raise it to the power of the total number of compounding periods:

(1 + r/n)^(nt) = (1 + 0.025)^(2×5) = (1.025)^10

Calculate the power of 1.025 to 10:

(1.025)^10 = 1.280084145

Finally, multiply this result by the principal amount to get the future value:

FV = 10,000 × 1.280084145 = $12,800.84

Round the future value to the nearest dollar which gives us $12,801

In conclusion, the $10,000 investment is worth $12,801 after five years with compound interest.