Answer:
The answer is B, 10%.
Explanation:
200 = (1 + i) 110
(1 + i)
2 +
121
(1 + i)
2
200 = (110 + 110i) + 121
(1 + i)
2
200 (1 + i)
2 = 110 + 110i + 121
200 ¡
1+2i + i
2
¢
= 231 + 110i
200 + 400i + 200i
2 = 231 + 110i
200i
2 + 290i − 31 = 0 (3)
From here, using the formula for the solution of a general quadratic equation,
ax2 + bx + c = 0 (4)
one can obtain
x1,2 = −b ± √b2 − 4ac
2a (5)
and thus
i1,2 = −290 ± p2902 − 4 × 200 × (−31)
2 × 200
The interest rate is bounded to be positive, by definition, so we would consider only the
positive of the two roots,
i = −290 + p2902 − 4 × 200 × (−31)
2 × 200
2
i = −290 + √84100 + 24800
400
i = −290 + √108900
400
i = −290 + 330
400
i = 40
400 = 1
10 = 0.1, i.e., 10%.
