Examkin

Question

Difficulty: MediumSimple Interest

To fund a certification course, a network administrator invested a specific amount of money into a standard savings account yielding 5%5\% annual simple interest. After leaving the funds untouched for 3030 months, the investment generated exactly $375\$375 in interest alone. What was the initial amount deposited into the account?

Answer: 3000 $

Answer

The initial amount deposited was $3,000.
The principal is found by dividing the interest earned by the product of the annual interest rate and the time in years. Converting 3030 months to 2.52.5 years and using the 5%5\% rate as 0.050.05, the calculation is 375÷(0.05×2.5)=3000375 \div (0.05 \times 2.5) = 3000.

Step-by-Step Solution

1
Identify the given variables for the simple interest formula.
I=375I = 375, r=0.05r = 0.05, t=30t = 30 months.
The formula requires these values to solve for the unknown principal PP.
2
Convert the time period from months to years.
t=3012=2.5t = \frac{30}{12} = 2.5 years.
The given interest rate is an annual rate, so the time must also be expressed in years.
3
Set up the simple interest equation.
375=P×0.05×2.5375 = P \times 0.05 \times 2.5
Using the standard simple interest formula I=P×r×tI = P \times r \times t.
4
Solve for the principal PP.
P=3750.125=3000P = \frac{375}{0.125} = 3000
Isolating PP provides the final initial deposit amount.

Key Concept

Calculating the principal using the simple interest formula over a fractional year term.
Rate this question

Topics

Simple Interest

More questions from this topic