Final answer:
The maturity value of a $100,000 investment at 7% interest, compounded semiannually for 4 years is approximately $131,707.76.
Step-by-step explanation:
To calculate the maturity value of an $100,000 investment at 7%, compounded semiannually for a 4-year period, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial sum 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.
Substituting the given values into the formula gives us:
A = 100000(1 + 0.07/2)^(2*4)
This simplifies to:
A = 100000(1 + 0.035)^(8)
A = 100000(1.035)^(8)
Calculating the exact value:
A ≈ 100000 * 1.3170776
A ≈ $131,707.76
So, the maturity value of the investment is approximately $131,707.76.