Evaluate $ 1500 ( 1 + 0.055 × 3 12 ) 1 + 0.10 × 9 12 \frac{\$ 1500\left(1+0.055 imes \frac{3}{12} ight) }{1+0.10 imes \frac{9}{12}} 1 + 0.10 × 12 9 $1500 ( 1 + 0.055 × 12 3 ) A) $1,414.53B) $1,843.18C) $348.85D) $454.56E) $1,625.58

Question

Evaluate   $ 1500 ( 1 + 0.055 × 3 12 )  1 + 0.10 × 9 12 \frac{\$ 1500\left(1+0.055 	imes \frac{3}{12}ight) }{1+0.10 	imes \frac{9}{12}} 1 + 0.10 × 12 9 ​ $1500 ( 1 + 0.055 × 12 3 ​ )  ​ A)  $1,414.53B)  $1,843.18C)  $348.85D)  $454.56E)  $1,625.58

Erick Sepulveda · Accepted Answer

Final Answer : A, Explanation :   The expression simplifies as follows: First, calculate the interest for 3 months at a 5.5% annual rate, then divide by the amount after applying a 10% annual rate for 9 months. Simplifying the expression gives:   1500 ( 1 + 0.055 × 3 12 ) 1 + 0.10 × 9 12 = 1500 ( 1 + 0.01375 ) 1 + 0.075 = 1500 × 1.01375 1.075 = 1520.625 1.075 ≈ 1414.53 \frac{1500(1+0.055 	imes \frac{3}{12})}{1+0.10 	imes \frac{9}{12}} = \frac{1500(1+0.01375)}{1+0.075} = \frac{1500 	imes 1.01375}{1.075} = \frac{1520.625}{1.075} \approx 1414.53 1 + 0.10 × 12 9 ​ 1500 ( 1 + 0.055 × 12 3 ​ ) ​ = 1 + 0.075 1500 ( 1 + 0.01375 ) ​ = 1.075 1500 × 1.01375 ​ = 1.075 1520.625 ​ ≈ 1414.53  .

Evaluate $1+0.10×912\frac{\$ 1500\left(1+0.055 \times \frac{3}{12}\right) }{1+0.10 \times \frac{9}{12}}$

A) $1,414.53
B) $1,843.18
C) $348.85
D) $454.56
E) $1,625.58

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Learning Objectives

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Evaluate $1500(1+0.055×312) 1+0.10×912\frac{\$ 1500\left(1+0.055 \times \frac{3}{12}\right) }{1+0.10 \times \frac{9}{12}}1+0.10×129​$1500(1+0.055×123​) ​ A) $1,414.53B) $1,843.18C) $348.85D) $454.56E) $1,625.58

Definitions

Learning Objectives

Learning Objectives

Related questions

Evaluate $1+0.10×912\frac{\$ 1500\left(1+0.055 \times \frac{3}{12}\right) }{1+0.10 \times \frac{9}{12}}$

A) $1,414.53
B) $1,843.18
C) $348.85
D) $454.56
E) $1,625.58