Chuck deposits $2000 into a bank account that compounds weekly at an annual interest rate of 15% Assuming there are no other transactions, what will the balance be after 10 years, in dollars?

Hi6942O May 26, 2024

#1**0 **

*Chuck deposits $2000 into a bank account that compounds weekly at an annual interest rate of 15% Assuming there are no other transactions, what will the balance be after 10 years, in dollars?*

Since the yearly interest rate for Chuck's account is 15% (same as 0**.**15) and there

are 52 weeks in a year, then the amount earned the first week is (2000)(0**.**15 / 52)

I'm going to change (0**.**15 / 52) to its decimal equal. I'll round that value to 0**.**00288

only for the convenience in writing it in this post. In my calculator I will not round it,

but maintain the entire 15-digit decimal in the calculations.

Since the bank is adding (0**.**00288) of the current balance to the account each week,

the total in the account (principal plus interest) after the first week is (2000)(1**.**00288).

Then each week, the balance is (1**.**00288) times what it was the week before.

Let's make a little tabulation, to demonstrate clearly the progression of the balance.

Balance at end of 1^{st} week (2000)(1**.**00288)

Balance at end of 2^{nd} week (2000)(1**.**00288)(1**.**00288)

Balance at end of 3^{rd} week (2000)(1**.**00288)(1**.**00288)(1**.**00288)

Balance at end of 4^{th} week (2000)(1**.**00288)(1**.**00288)(1**.**00288)(1**.**00288)

Balance at end of n^{th} week (2000)(1**.**00288)^{n}

Balance at end of 520^{th} week (2000)(1**.**00288)^{520} = **8944.04** dollars

_{.}

Bosco May 26, 2024