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Question

Difficulty: MediumSimple Interest

A college student invests $2,500\$2,500 of their scholarship money into a bank savings certificate that pays an annual simple interest rate of 3.6%3.6\%. How many months will it take for the investment to earn exactly $135\$135 in interest?

Answer: 18 months

Answer

18
The simple interest formula is I=P×r×tI = P \times r \times t. Substituting the given values gives 135=2500×0.036×t135 = 2500 \times 0.036 \times t. Solving for tt yields 1.51.5 years. Multiplying by 12 converts this to exactly 18 months.

Step-by-Step Solution

1
Identify the simple interest formula and the given values.
I=P×r×tI = P \times r \times t, where I=$135I = \$135, P=$2,500P = \$2,500, and r=0.036r = 0.036.
To set up the equation to solve for the unknown time variable.
2
Substitute the values into the formula and simplify.
135=2500×0.036×t135 = 2500 \times 0.036 \times t, which simplifies to 135=90t135 = 90t.
To isolate the term with the unknown variable.
3
Solve for the time tt in years.
t=135/90=1.5t = 135 / 90 = 1.5 years.
The standard simple interest formula calculates time in years.
4
Convert the time from years to months.
1.5×12=181.5 \times 12 = 18 months.
The question specifically asks for the duration in months.

Key Concept

Simple Interest
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Topics

Simple Interest

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