As an incentive to attract savings deposits, most financial institutions today offer daily and even continuous compounding. This means that savings, or passbook, accounts, as well as certificates of deposit $($CDs$),$ earn interest compounded each day or even more frequently, such as every hour or even every minute. $($Continuous compounding, in which compounding occurs every instant, involves a different formula that is derived from the formula we've been using.$)$ Let's take a look at daily compounding.

To calculate the compound amount, A$,$ of an investment with daily compounding, use the compound interest formula modified as follows:

Rate per period $($daily$)=$

i

$365$

$($nominal interest rate, i$,$ divided by $365)$

Number of periods $($days$),$ n$,=$ number of days of the investment.

A $=$ P$$

$1+$

i

$365$

n

Calculator Sequence:

$(1+($ i $-$: $365))$ yx n $$ P $=$ A$.$

$($Round your answers to the nearest cent.$)$

$($a$)$

On April $12,$ Thomas Ash deposited $$2,300$ in a passbook savings account at $3\mathrm{.}5\%$ interest compounded daily. What is the compound amount $($in $$)$ of his account on August $5?$

$

$($b$)$

Using daily compounding, calculate the compound amount $($in $$)$ of a $$9,000$ investment for each of the three CDs$.$

The First National Bank is offering a $5$ year CD at $3\%$ interest.

The Second National Bank is offering a $5$ year CD at $4\%$ interest.

The Third National Bank has a $5$ year CD at $5\mathrm{.}5\%$ interest.

First National Bank $

Second National Bank $

Third National Bank $