Given:
Number of days the loan lasted = 292 days
annual rate of interest =2.5%
Total interest paid = $146
Required: The amount David borrowed
Let the amount David borrowed be x
To solve the problem, we have the apply the simple interest formula:
[tex]\begin{gathered} Interest\text{ = }\frac{principal\text{ }\times\text{ rate }\times\text{ time}}{100} \\ Where\text{ time is in years} \end{gathered}[/tex]
Converting the time in days to years:
[tex]\begin{gathered} =\text{ 292 days }\times\text{ }\frac{1\text{ year}}{365\text{ days}} \\ =\text{ 0.8 yr} \end{gathered}[/tex]
Substituing the given values and solving for x:
[tex]\begin{gathered} 146\text{ = }\frac{x\text{ }\times\text{ 2.5}\times0.8}{100} \\ Cross-Multiply \\ 2x\text{ = 14600} \\ Divide\text{ both sides by 2} \\ x\text{ = 7300} \end{gathered}[/tex]
Hence, David borrowed $7300
