Pat plans to buy a new $1,000 stereo for Christmas 1999. What lump sum should she deposit at
6% compounded monthly so that she can afford her new stereo a year and a half from now?

Please help with step by step

she should deposit $914.16

Step-by-step explanation:

We would apply the formula for determining compound interest which is expressed as

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

Where

A = total amount in the account at the end of t years

r represents the interest rate.

n represents the periodic interval at which it was compounded.

P represents the principal or initial amount deposited

From the information given,

r = 6% = 6/100 = 0.06

n = 12 because it was compounded 12 times in a year.

t = 1.5 years

A = $1000

Therefore,.

1000 = P(1+0.06/12)^12 × 1.5

1000 = P(1 + 0.005)^18

1000 = P(1.005)^18

1000 = 1.0939P

P = 1000/1.0939

P = $914.16