- Calculate the balance after year 1 using the 3% interest rate: \(960,000 \times 1.03 = 988,800\).
- Calculate the balance after year 2 using the 4% interest rate: \(988,800 \times 1.04 = 1,028,352.00\).
- Calculate the balance after year 3 using the 5.5% interest rate: \(1,028,352 \times 1.055 = 1,084,911.36\).
- The final balance at the end of the third year is \(\boxed{\text{N}1,084,911.36}\).
Explanation
- Analysis of the Investment Problem
We start with a principal amount of \(\text{N}960,000\). This amount is invested for three years with compound interest calculated annually. The annual interest rates are \(3\%\) for the first year, \(4\%\) for the second year, and \(5.5\%\) for the third year. Our objective is to determine the total balance at the end of the three-year period by applying these rates sequentially.
- Calculating the Balance After Year 1
To find the balance after the first year, we multiply the principal by \((1 + r_1)\), where \(r_1 = 3\% = 0.03\).
The calculation is:
\[A_1 = 960,000 \times (1 + 0.03) = 960,000 \times 1.03 = 988,800.\]
After the first year, the balance is \(\text{N}988,800\).
- Calculating the Balance After Year 2
For the second year, the new balance \(A_1\) earns interest at a rate of \(r_2 = 4\% = 0.04\).
The calculation is:
\[A_2 = 988,800 \times (1 + 0.04) = 988,800 \times 1.04 = 1,028,352.\]
Rounding to two decimal places, the balance after the second year is \(\text{N}1,028,352.00\).
- Calculating the Final Balance After Year 3
For the third year, the balance \(A_2\) earns interest at a rate of \(r_3 = 5.5\% = 0.055\).
The calculation is:
\[A_3 = 1,028,352 \times (1 + 0.055) = 1,028,352 \times 1.055 = 1,084,911.36.\]
Rounding to two decimal places, the balance after the third year is \(\text{N}1,084,911.36\).
Examples
In real life, compound interest is the engine behind savings and investments. For instance, if you deposit money into a high-yield savings account or invest in a bond fund with varying market interest rates, the interest you earn each year is added to your account balance, and the following year you earn interest on that new, larger amount. This process allows your money to grow exponentially over time, which is essential for long-term financial planning, such as saving for retirement or a college education.