5) Horatio Reyes earns 3.625% interest on his account. If his principal is $6000 and he deposits $150 into the account every 6 days, how much total

interest will Horatio earn after 30 days? *

$20.11

Step-by-step explanation:

Solution:-

- We will define the interest rate ( R ) earned on his deposits in the account per annum ( 365 days ).

- He deposits a principal amount of ( P ) = $6,000 once at the start of the accounting period.

- After the principal amount is deposited he deposits $ 150 in the account after every 6 days.

- We will first determine the amount in his account at the end of 30 days.

- We need to see how many additional deposits of $150 were made in these 30 days.

- The ( n ) number of additional deposits can be determined from the ratio of time-span of each deposition and the total accounting period:

- Horatio Reyes makes ( n = 5 ) additional deposits after the principal amount till the end of 30th day.

- Now we can calculate the total amount accumulated ( A ) in his account at the end of 30 days time period. It comprises of the initial principal amount and the 5 series of $150 deposits:

- Plug in the respective amounts ( P and n ):

- At the end of 30th day Horatio Reyes has $6,750 in his account.

- The interest rate ( r ) applied at the end of the 30-day time period is sub-part of the total interest rate ( R ) applied per annum.

- So the interest rate applied at the end of 30-day tim period is determined from simple proportional ratios of time-period:

                      Rate(%)                     Time(days)

               R:   3.625                             365        

               r:       x                                   30

     ========================================

                      x = 30*3.625 / 365 = 0.29795%

     ========================================

- Now we will apply the rate ( r ) on the accumulated amount ( A ) by the end of 30-day time period in the account to determine the interest earned ( I ):

- The amount of interest earned ( I ) is $20.11 after 30 days.

t= half of the arc subtended by t.

r= half of the arc subtended by r.  

t+r= half of the arc subtended by t + half of the arc subtended by r= half of 360=180

step-by-step explanation:

b is the right answer