An investor allocates a sum of money between two financial products, Account A and Account… — GMAT

An investor allocates a sum of money between two financial products, Account A and Account B. Account A yields an annual simple interest rate of $6\%$ , while Account B yields an annual simple interest rate of $10\%$ . After one year, the total interest earned from both accounts combined is $\$2,600$ . If the amount invested in Account B is exactly twice the amount invested in Account A, select the value that corresponds to the amount invested in Account A and the value that corresponds to the amount invested in Account B.

Amount invested in Account A $\$10,000$
Amount invested in Account B $\$20,000$

Answer

The amount invested in Account A is

\$10,000

and the amount invested in Account B is

\$20,000

Solving the simultaneous system

0.06x + 0.10y = 2,600

and

y = 2x

yields

0.26x = 2,600

, resulting in

x = \$10,000

for Account A and

y = \$20,000

for Account B.

Step-by-Step Solution

Define variables and formulate the system of equations based on interest earned and relative investment ratio.

Let

x

be the amount in Account A and

y

be the amount in Account B. The problem statements give: (1)

0.06x + 0.10y = 2,600

and (2)

y = 2x

Translating word constraints into algebraic representations sets up a two-variable system.

Substitute equation (2) into equation (1) to solve for

x

0.06x + 0.10(2x) = 2,600 \implies 0.06x + 0.20x = 2,600 \implies 0.26x = 2,600 \implies x = 10,000

Substitution simplifies the simultaneous system into a single linear equation in terms of

x

Calculate

y

using the relationship

y = 2x

y = 2(10,000) = 20,000

Multiplying the value of

x

by 2 gives the value for Account B.

Key Concept

Simultaneous Linear Equations by Substitution

Question

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Step-by-Step Solution

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