Final answer:
To calculate the maturity value of the investment, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the maturity value, P is the principal amount, r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years the investment matures. In this case, the maturity value is approximately $64,912.57.
Step-by-step explanation:
To calculate the maturity value of the investment, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the maturity value, P is the principal amount, r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years the investment matures.
In this case, the principal amount is $54542.16, the interest rate is 2.9% per annum, compounded semi-annually, and the investment matures in 6 years and 2 months.
Substituting the given values into the formula, we have A = 54542.16(1 + 0.029/2)^(2*(6 + (2/12))).
Calculating the exponential part first, we get (1 + 0.029/2)^(2*(6 + (2/12))) ≈ (1.0145)^(2*(6.17)) ≈ (1.0145)^12.34 ≈ 1.188262.
Now, we can multiply the principal amount by the exponential part to find the maturity value: A ≈ 54542.16 * 1.188262 ≈ $64,912.57. Therefore, the maturity value is approximately $64,912.57.