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Difficulty: MediumSimple Interest

A graphic designer places $8,000\$8,000 into a high-yield savings certificate that pays an annual simple interest rate of 4.5%4.5\%. Upon maturity, the account has generated exactly $270\$270 in interest. How many months was the money invested?

  1. A
    0.75
  2. B
    7.5
  3. 9Answer
  4. D
    12

Answer

The money was invested for exactly 9 months.
The investment earns $360\$360 in a full year ($8,000×0.045=$360\$8,000 \times 0.045 = \$360). Since the actual interest earned is $270\$270, the time in years is 270/360270 / 360, which simplifies to 3/43/4 or 0.750.75 years. Multiplying 0.750.75 years by 1212 months per year gives exactly 99 months.

Step-by-Step Solution

1
Identify the given variables and the simple interest formula.
Principal (PP) = $8,000\$8,000, Interest (II) = $270\$270, Rate (rr) = 4.5%4.5\% or 0.0450.045. The formula is I=P×r×tI = P \times r \times t.
Setting up the standard formula is the first step to isolate and find the unknown time variable.
2
Calculate the amount of interest earned in one full year.
$8,000×0.045=$360\$8,000 \times 0.045 = \$360 per year.
Finding the annual interest provides the denominator needed to determine what fraction of a year the money was invested.
3
Divide the actual interest earned by the annual interest to find the time in years.
$270/$360=0.75\$270 / \$360 = 0.75 years.
The ratio of earned interest to annual interest gives the exact time the money remained in the account in years.
4
Convert the time from years into months.
0.75 years×12 months/year=9 months0.75 \text{ years} \times 12 \text{ months/year} = 9 \text{ months}.
The question specifically asks for the time duration in months, requiring a final unit conversion.

Key Concept

Calculating the time duration of an investment using the simple interest formula and converting the resulting fractional year into months.
Estimated Time:1m 30s
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Topics

Simple Interest

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