Final answer:
To determine the total interest earned by March 2025, compound interest formula must be applied to each period of investment separately and then combined. The calculation involves finding the accumulated amount after the first five years of investment and reinvesting that total at a different interest rate for the remaining period until 2025.
Step-by-step explanation:
The student's question pertains to calculating the total interest earned through compound interest across two different investments over a specific period of time. In the first investment, Natalie invested $800 at a 4.8% annual interest rate, compounded monthly, for 5 years. After 5 years, she reinvested the total amount at a 6% annual interest rate, compounded semiannually, until March 2025. To solve this, we apply the compound interest formula A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount, r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested or borrowed for, in years.
First calculation for the period from March 2003 to March 2008:
A1 = 800(1 + 0.048/12)^(12*5)
For the second investment, we need to calculate the time from March 2008 to March 2025, which is 17 years. Assuming the total amount from the first investment (A1) is reinvested:
A2 = A1(1 + 0.06/2)^(2*17)
Finally, to find the total interest earned by March 2025, we will subtract the initial investment from the final amount:
Total Interest = A2 - 800
All the calculations above will use algebraic manipulation and a calculator to determine the final amount from each investment. To fully answer the student's question, you would calculate A1, use that result to calculate A2, and then subtract the original principal from A2.