Help me with this question (in description)

Question

Tricia has $1500 in her bank account. She wants to buy a CD player and invest the remainder at 6 1/2% compounded quarterly for 4 years. At the end of the 4 years, Tricia wants $1500 in her bank account. Approximately how much can Tricia spend on the CD player?

Answer 1

The regular form of an exponential equation with compounded interest is A=A₀(1+r/n)t*n where n is the compounding periods, A₀ is the initial amount, r is the rate per year in decimal form, and t is the number of years. In this case, the initial amount is (1500 - c) where c is the amiunt spent on a CD player.

So: 1500 = (1500 - c)(1+0.065/4)^4*4

1500 = (1500 - c)(1.01625)¹⁶

1500 = (1500 - c)(1.294222)

1500/1.294222 = 1500 - c

1158.997 = 1500 - c

c = 1500 - 1158.997 = $341