Question

a student borrows $3000 at 15% for 6 months to pay tuition. find the total amount due using simple interest. total amount due after 6 months is: $________

Answer 1

The total amount due after a given period of time is given by the following formula:

$A=P(1+rt)$

This is for simple interest. A is the total amount due. t is the period of time, r is the interest rate and P is the initial amount borrowed.

To use the formula, t and r must have the same unit of time (both in years or both in months for example). We have the yearly rate as 15%, or well, 0.15. The period is 6 months, which will be half a year, or well, 0.5 years. With this information, we can now replace the values on the formula:

$\begin{gathered} A=3000\cdot(1+0.15\cdot0.5) \\ A=3225 \end{gathered}$

With this, the total amount due will be $3225.

Alternatively, we can first calculate the interest due with the following formula:

$I=P\cdot r\cdot t$

And add this amount to the initial amount of money borrowed to estimate the total amount due.

$\begin{gathered} I=3000\cdot0.15\cdot0.5 \\ I=225 \end{gathered}$

After six months, the student has to pay the $3000 borrowed, plus $225 of interest:

$\begin{gathered} A=3000+225 \\ A=3225 \end{gathered}$

Answer. Total amount due after 6 months: $3225.