Question

Approximately how much principal would need to be placed into an account earning 3.575% interest compounded quarterly so that it has an accumulated value of $68,000 at the end of 30 years

Answer 1

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