Please help, I will give Brainliest!

After retiring, Mary wants to be able to take $1500 every quarter for a total of 20 years from her retirement account. The account earns 4% interest. How much will she need in her account when she retires?

If you could also give step by step, thank you!!!

she would need $123775.5 in her account when she retires.

Step-by-step explanation:

We would apply the formula for determining future value involving constant deposits at constant intervals. It is expressed as

S = R[{(1 + r)^n - 1)}/r][1 + r]

Where

S represents the future value of the investment.

R represents the regular payments made(could be weekly, monthly)

r = represents interest rate/number of payment intervals

n represents the total number of payments made.

From the information given,

Since she would be taking $1500 four times in a year, then

R = 1500

r = 0.04/4 = 0.01

n = 3 × 20 = 60 times in 20 years

Therefore,

S = 1500[{(1 + 0.01)^60 - 1)}/0.01][1 + 0.01]

S = 1500[{(1.01)^60 - 1)}/0.01][1.01]

S = 1500[{(1.817 - 1)}/0.01][1.01]

S = 1500[0.817/0.01][1.01]

S = 1500[81.7][1.01]

S = 1500 × 82.517

S = 123775.5