Question

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

Answer 1

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

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