Use the compound interest formula to compute the balance in the following account after the stated period of​ time, assuming interest is compounded annually. ​$6000 invested at an APR of 2.5​% for 20 years.

Most financial institutions use one of two methods to calculate interest on investments. These are simple and compound interest.
Simple interest is only computed on the principal amount. Compound interest, on the other hand, is computed on the principal and interest accrued.
The Compound Interest Formula is A(t) = P(1 + r/n)^(nt)
where:
A(t) is the amount in the bank after a certain period of time
P is the principal
r is the yearly rate of interest
n is the number of compounding periods in a year, and
t is the number of years.
In this case,
P = $6000
r = 2.5 % = 0.025
n = 1
t = 20
We plug these values into the Compound Interest Formula to get:
A(t) = 6000(1.025)^20 = $9831.70

Therefore, the total amount in the bank after 20 years is $9831.70.

Compound interest is the addition of interest to the principal investment. We could also say that it is "the interest on interest"—that is, interest is earned on the principal sum plus previously accumulated interest.
Using the concept of compound interest, we have to find the balance, or accumulated amount, in the account after 20 years when compounded annually.
The compound interest formula is given by:
Final Amount accumulated = A = P(1+r/n)^(nt)
where P = principle amount
r = annual rate of interest
t = total period of investment in years
and n = number of times interest is compounded per year.
Here, we are given that
P = $6000
r = 2.5% = 0.025
t = 20 years
n = 1, since interest is compounded annually.
Therefore, using the compound interest formula, we have
A = 6000(1+0.025)^20
= 6000(1.025)^20
= 6000(1.6386)
= 9831.70
Hence, total balance accumulated in the account after 20 years, invested at the rate of 2.5%, is $9831.70.