SAT Mathematics Practice Test 4

Question : 34 of 58

Marks: +1, -0

1,000(1+r/{1,200})^12

The expression above gives the amount of money, in dollars, generated in a year by a $1,000 deposit in a bank account that pays an annual interest rate of r %, compounded monthly. Which of the following expressions shows how much additional money is generated at an interest rate of 5% than at an interestrate of 3% ?

$1,000(1+{5-3}/{1,200})^12$
$1,000(1+{5/3}/{1,200})^12$
${1,000(1+5/{1,200})^12}/{1,000(1+3/{1,200})^12}$
$1,000(1+5/{1,200})^12-1,000(1+3/{1,200})^12$

Validate

Solution:

According to the given formula, the amount of money generated for a year at 5% interest, compounded monthly, is

1,000(1+5/{1,200})^12

, whereas the amount of money generated at 3% interest, compounded monthly, is

1,000(1+3/{1,200})^12

. Therefore, the difference between these two amounts,

1,000(1+5/{1,200})^12-1,000(1+3/{1,200})^12

, shows how much additional money is generated at an interest rate of 5% than at an interest rate of 3%.
Choices A, B, and C are incorrect and may be the result of misinterpreting the given formula. For example, the expression in choice C gives how many times as much money, not how much additional money, is generated at an interest rate of 5% than at an interest rate of 3%.

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