Dan borrowed $750.00 from his brother with a 5% simple interest. if dan pays his brother back in 6 months, how much does he have to pay back including the interest?

$780

Step-by-step explanation:

The initial sum of money borrowed was $750

at a simple interest rate of 8%

Dan pays the money back in 6 months

The amount of money Dan has to pay back his brother including the interest in 6 months' time.

The total amount accrued, principal plus interest, from simple interest on a principal of $750 at a rate of 8% per year for 6 months is $780.

The total interest that is to be paid back can be calculated using the formula

where P is the prinicipal amount of money we begin with (in this case $750), r is the rate of interest (in this case 8%) and t is the time period (in this case, 6 months or 1/2 of a year).

(Note that we must take the value of t in years if the interest is annual interest and that is why we use t = 1/2 = 0.5 instead of t = 6).

So, by simple calculation we can find interest to be paid as

the interest accrued is $30

To find the total sum to be paid back, we add the initial sum or pricipal amount to the interest we have calculated above i.e.,

the total amount accrued, principal plus interest, from simple interest on a principal of $750 at a rate of 8% per year for 6 months is $780.