Final answer:
To find the maturity value for $1550 compounded annually at 6.75% for 23 months, we apply the compound interest formula. The calculation reveals that the maturity value is approximately $1756.72, which corresponds to option C.
Step-by-step explanation:
The subject of the question is compounding interest, which falls under the Mathematics category. The grade level is most likely High School, where students begin to learn about more complex financial mathematics.
To determine the maturity value of the investment, we use the compound interest formula, which is A = P(1 + r/n)^(nt). Here, A is the amount of money accumulated after n years, including interest. P is the principal amount ($1550), r is the annual interest rate (6.75%, which is 0.0675 as a decimal), n is the number of times that interest is compounded per year (annually, so n=1), and t is the time the money is invested for, in years (23 months is approximately 1.92 years).
Step-by-Step Calculation:
- Convert the annual interest rate from percentage to a decimal: 6.75% = 0.0675.
- Since the compounding is annual, n = 1.
- Convert the time period from months to years: 23 months / 12 = 1.92 years.
- Use the compound interest formula: A = 1550(1 + 0.0675/1)^(1*1.92).
- Calculate the amount: A = 1550(1 + 0.0675)^(1.92).
- Approximate the maturity value: A ≈ 1550(1.0675)^1.92.
- Compute the maturity value, which will be closest to one of the provided options.
By doing the calculation, we find that the maturity value is closest to the option C: $1756.72.