Final answer:
To determine Monica's investment's accumulated value, we use the future value of a series formula for compound interest. The accumulated value after the first 4 years and the final value at the end of 11 years are determined separately, considering the two different interest rates. Finally, the amount of interest earned is found by subtracting the total contributions from the final accumulated value.
Step-by-step explanation:
To find the accumulated value of Monica's investment after the first 4 years, we use the future value of a series formula for compound interest. The formula is: FV = P × ((1 + r)n - 1) / r, where P is the regular investment amount, r is the interest rate per period, and n is the total number of periods.
For the first 4 years (which is 8 periods because Monica invests every 6 months),
- P = $2,100
- r = 4.40% per annum compounded semi-annually → 0.044 / 2 = 0.022 per period
- n = 4 years × 2 = 8 periods
Thus, the future value (FV) after 4 years is calculated as:
FV = 2100 × ((1 + 0.022)8 - 1) / 0.022
For the next 7 years with a different interest rate,
- r = 5.20% per annum compounded semiannually → 0.052 / 2 = 0.026 per period
- n = 7 years × 2 = 14 periods
- The calculated FV from the first 4 years becomes the principal for the next calculation.
The final FV, including the first 4 years of investments and the next 7 years, would then be the sum of the second FV calculation plus the FV after 4 years, multiplied by (1 + 0.026)14.
To calculate the total amount of interest earned, subtract the total contributions from the final FV.