The value at 10 years given an interest rate of 5% in 3 years and 4% in
the 7 years is 10.007 times one of the annual payments.
Interest in the first year = 5% = 0.05
Let P represent the annual payments
The amount in the investment are as follows;
In the first three years are;
Amount at the start of the 1st year = P
Amount at the start of the 2nd year = P + P + (0.05·P) = 2.05·P
Amount at the start of the 3rd year = P + 2.05·P + 2.05·P × 0.05 = 3.1525·P
After the 5 years of equal payment, we have;
The future value
[tex]FV =\mathbf{3.1525\cdot P \times (1+0.04)^5 + P \times \left[\dfrac{(1 + 0.04)^5 - 1}{0.04} \right]}= 9.252 \cdot P[/tex]
At 10 years, we have;
[tex]Value \ of \ investment = 9.252 \cdot P \times (1 + 0.04)^2 \approx \underline{10.007 \cdot P}[/tex]
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