Determine the missing principal amount based on the given simple interest details. Fill in… — Armed Services Vocational Aptitude Battery (ASVAB)

Determine the missing principal amount based on the given simple interest details. Fill in the blank with the correct numeric value.

Answer:A homeowner paid

\$210

in simple interest on a short-term loan that lasted

14

months. If the loan had a

4\%

annual simple interest rate, the original principal amount borrowed was \$【4500】.

The original principal amount borrowed was

\$4,500

The correct principal is found by rearranging the simple interest formula to

P = \frac{I}{R \times T}

. By converting the

14

months into

\frac{7}{6}

years and using the decimal rate of

0.04

, dividing the

\$210

interest by their product yields the original principal of

\$4,500

Identify the known values: Interest (

I

), annual Rate (

R

), and Time (

T

) in months.

I = 210

R = 0.04

, and

T = 14

months

These are the given variables needed to set up the simple interest equation.

Convert the loan duration from months into years.

T = \frac{14}{12} = \frac{7}{6}

years

The simple interest formula requires time to be in years when the given interest rate is annual.

Substitute the values into the simple interest formula (

I = PRT

) to isolate Principal (

P

210 = P \times 0.04 \times \frac{7}{6}

This establishes the equation with only one unknown variable.

Calculate the product of the rate and time, then divide the total interest by this product.

P = \frac{210}{\frac{0.28}{6}} = 210 \times \frac{6}{0.28} = \frac{1260}{0.28} = 4500

Simplifying the expression yields the exact borrowed amount.

Solving for the principal using the simple interest formula

I = PRT

by converting time in months to a fraction of a year.

Question