If a is the initial amount put into an account, p is the annual percentage rate of interest, which remains fixed, and the account compounds quarterly, which of the following is an expression, in terms of a and p, for the amount in the account after 5 years?
a 4a(p100)5
b a(p100)20
c 4a(1+p100)5
d a(1+p25)20
e a(1+p400)20

The amount in the account is A = A(1 + P/400)^20

Step-by-step explanation:

Initial amount deposited into the account is A. This means that the principal is A, so

P = A

It was compounded quarterly. This means that it was compounded once in four months. So

n = 4

The rate at which the principal was compounded is P%. So

r = P/100

It was compounded for a total of 5 years. So

n = 5

The formula for compound interest is

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

A = total amount in the account at the end of n years.

Let A = B

B = A(1 + (P/100)/4)^4×5

A = A(1 + P/400)^20

it's