Answer: 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