We are given an initial deposit of $5,000 in an account that pays 7.1% annual interest (apr). We are asked to find the amount in the account after five years if the account pays interest compounded annually.

The formula to use is `A=P(1+r/n)^(nt)` where:
A is the amount in the account at time t
P is the principal or initial deposit
r is the annual interest rate (apr) as a decimal
n is the number of compounding periods per year
t is the time in years.

Here P=$5,000, r=.071, n=1 (annual means once per year), and t=5.

Then `A=5,000(1+.071)^5~~7,045.589863` or A=$7,045.59.

Initial deposit is $5,000. At the end of the year, the account accrues 7.1% interest or 5,000(.071)=$355. This is the same as 5,000(1.071).

At the end of the second year, interest is paid on the entire $5,355; so interest of $380.21 is paid to the account for a total of $5,735.21. Note that this is equivalent to 5,000(1.071)(1.071)=5000(1.071)^2.

At the end of five years there will be 5,000(1.071)^5=7045.59.

If there were more compounding periods, the amount would be larger.

If the account were paid biannually (twice a year), then n=2 and we get
`5,000(1+.071/2)^(2*5)~~7,087.14`

If the account were paid quarterly, then n=4 and we get
`5,000(1+.071/4)^4*5)~~7,108.73`

If the account were paid monthly, then n=12 and we get
`5,000(1+.071/12)^(12*5)~~7,123.45`