Marcus is comparing two personal bank loan options to finance home repairs. Option X offer… — Armed Services Vocational Aptitude Battery (ASVAB)

Marcus is comparing two personal bank loan options to finance home repairs. Option X offers a $\$4,000$ loan at an annual simple interest rate of $6\%$ for $18$ months. Option Y offers a $\$5,000$ loan at an annual simple interest rate of $4\%$ for $9$ months. How much more interest will Marcus pay with Option X compared to Option Y?

$\$210$ Answer
B
$\$252$
C
$\$2,100$
D
$\$2,520$

Answer

\$210

The correct answer accurately converts both time periods into years and applies the simple interest formula (

I = P \times R \times T

) to find the interest for both loans before calculating their difference. Option X generates

\$360

in interest (

4000 \times 0.06 \times 1.5

), and Option Y generates

\$150

in interest (

5000 \times 0.04 \times 0.75

). The difference is

\$360 - \$150 = \$210

Step-by-Step Solution

Convert the loan durations from months to years by dividing by 12.

Option X time:

18 \div 12 = 1.5

years. Option Y time:

9 \div 12 = 0.75

years.

The simple interest formula requires the time to be in the same units as the annual interest rate.

Calculate the total simple interest for Option X using

I = P \times R \times T

I_X = \$4,000 \times 0.06 \times 1.5 = \$360

This determines the exact cost of borrowing for the first option.

Calculate the total simple interest for Option Y using

I = P \times R \times T

I_Y = \$5,000 \times 0.04 \times 0.75 = \$150

This determines the exact cost of borrowing for the second option.

Subtract the interest of Option Y from the interest of Option X.

\$360 - \$150 = \$210

The question asks for the difference in interest paid between the two options.

Key Concept

Calculating and comparing simple interest across different principals, rates, and fractional year time periods.

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