Answer: the principal is approximately 23377
Step-by-step explanation:
Let the Initial amount deposited into the account be $x This means that the principal is P = $x
It was compounded quarterly. This means that it was compounded four times in a year. So
n = 4
The rate at which the principal was compounded is 3.575%. So
r = 3.575/100 = 0.03575
It would be compounded for 30 years So
t = 30
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 given as $68,000
Therefore
68000= x (1+0.03575/4)^4×30
68000= x (1+0.0089375)^120
68000= x (1.0089375)^120
68000 = 2.90878547719x
x = 68000/2.90878547719
x = 23377.4545
