Question

HELP ME PLEASE
Olga deposited $1500 in a savings account that pays 7.5% interest compounded quarterly. What is the balance in her account at the beginning of the third quarter?
A. $1,590
B. $1,560
C. $1,585.97
D. $1,591.81
ok let me make one thing clear: i have put up questions like this before but i am NOT TRYING TO JUST GET ANSWERS. I legit want to learn this. It is just hard for me i guess.. so sorry if this answer seems simple to you but its not to me so if you could please explain your answer CLEARLY, in particular with "compound quarterly." please explain so i can use the principles later on. Thank you!

Answer 1

Let P be the final value
Let r be the rate
Let t be the time in years
Let C be the initial value
Let n be the number of times interest is given per year

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

r = 0.075 (7.5%)
t = 3/4 years
C = $1500
r = 4 (4 quarters in one year)

P = C (1+r/n)^ (t/n)
= 1500 * (1 + 0.075/4) ^ (3/4 * 4)
= 1585.97

Have an awesome day!

If you are wondering, a quarter means 1/4 of a year.