I don't know how to solve this problem, Please Help!

Question

Suppose that ​$2000 is deposited at 6​% compounded quarterly. ​

(a) How much money will be in the account at the end of 7 ​years? (Assume no withdrawals are​ made.)

​(b) How long will it take for the account to grow to ​$3000​?

​(c) The account will contain ​$nothing at the end of 7 years.

Answer 1

The formula for compound interest is:

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

Where:

A = final amount

P = Principal

r = annual rate

n = number of times the money is compounded in a year.

Given:

P= 2000

r = 6% = .06

n= 4 (for quarterly)

(a) t = 7. Looking for A.

A =2000(1+.06/4)⁽⁴⁾⁽⁷⁾

A = $3034.44

(b) 3000 = 2000(1+.06/4)^4t

1.5 = (1.015)^4t

ln (1.5) = 4t•ln (1.015)

t =ln (1.5)/(4•ln (1.015))

t≈ 6.81 years