Respuesta :
Answer:
$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:
[tex]n = \frac{30}{6} = 5[/tex]
- 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:
[tex]A = P + $150*n[/tex]
- Plug in the respective amounts ( P and n ):
[tex]A = 6000 + 150*5\\\\A = 6000 + 750\\\\A = 6750[/tex]
- 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
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x = 30*3.625 / 365 = 0.29795%
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- 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 ):
[tex]I= \frac{r*A}{100} \\\\I = \frac{0.29795*6750}{100} \\\\I = 20.111[/tex]
- The amount of interest earned ( I ) is $20.11 after 30 days.
