If $500 is deposited in a savings account providing an annual interest rate 5.6% compounded quarterly, how long will it take for the account to be worth $750

Answer:it will take 5 years

Step-by-step explanation:

Initial amount deposited into the account is $500 This means that the principal is

P = 500

It was compounded quarterly. This means that it was compounded 4 times in a year. So

n = 1

The rate at which the principal was compounded is 5.6%. So

r = 5.6/100 = 0.056

The formula for compound interest is

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

A = total amount in the account at the end of t years. A is already given as $750

Therefore,

750 = 500 (1+0.056/4) ^4*t

750 = 500 (1+0.014) ^4t

750 = 500 (1.014) ^4t

(1.014) ^4t = 750/500 = 1.5

Take root 1/4 of both sides

(1.014) ^4t * 1/4 = 1.5^1/4

(1.014) ^t = 1.107

t = 5 years