an amount of 1000 is deposited in a bank that pays 8% interest/year compounded daily (take the number of days in a year to be 365)

let an denote the total amount on deposit after n days, assuming no deposits or withdrawals are made during the period in question
a. find the formula for an
b. compute a1, a10. a50 and a100
c. what amount is on deposit after 1 year?

compounded daily?

an=1000(1+0.08/365)^t where t is in days.

for instance, after 100 days, put this in your google search window:

1000(1+0.08/365)^100=

To solve this problem, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:
A is the total amount on deposit after n days.
P is the principal amount (initial deposit) which is $1000 in this case.
r is the annual interest rate expressed as a decimal, which is 8% or 0.08.
n is the number of times the interest is compounded per year, which is daily (365 times).
t is the time in years, which we'll calculate in terms of days.

a. Formula for an:
Using the compound interest formula, the formula for an becomes:

an = 1000(1 + 0.08/365)^(365n)

b. Computing a1, a10, a50, and a100:
To compute a1, a10, a50, and a100, plug the respective values of n into the formula:

- a1 = 1000(1 + 0.08/365)^(365*1)
- a10 = 1000(1 + 0.08/365)^(365*10)
- a50 = 1000(1 + 0.08/365)^(365*50)
- a100 = 1000(1 + 0.08/365)^(365*100)

c. Amount after 1 year:
To find the amount after one year, substitute n = 1 into the formula:

Amount after 1 year = 1000(1 + 0.08/365)^(365*1)

Now, let's calculate the values of a1, a10, a50, a100, and the amount after 1 year using these formulas.