⚡ AZUCATION SHORTCUT:
Always use options for installment questions!
Test 8%:
$1000 \xrightarrow{+8\%} 1080 \xrightarrow{-530} 550$.
$550 \xrightarrow{+8\%} 550 + 44 = \mathbf{594}$.
Matches exactly. Answer is 8%.

Method: Present Value Equivalence
The loan amount must be equal to the sum of the present values of the installments.
Let the multiplying factor be $k = (1 + \frac{r}{100})$.
$$1000 = \frac{530}{k} + \frac{594}{k^2}$$ Multiply by $k^2$:
$1000k^2 - 530k - 594 = 0$
$500k^2 - 265k - 297 = 0$
Solving for $k$ using the quadratic formula or substituting options:
For $k = 1.08$:
$500(1.1664) - 265(1.08) - 297 = 583.2 - 286.2 - 297 = 0$.
Since $k = 1.08$, the rate is $\mathbf{8\%}$.

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