Question

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? *

Answer 1

$20.11

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:

`n = (30)/(6) = 5`

- 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:

`A = P + $150*n`

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

`A = 6000 + 150*5\\\\A = 6000 + 750\\\\A = 6750`

- 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 ):

`I= (r*A)/(100) \\\\I = (0.29795*6750)/(100) \\\\I = 20.111`

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