Round any decimals to the nearest penny.
Your fixed expenses are $1,763.25/month. You saved 6 months' worth for an emergency fund in a savings account earning a 4.5% APR over 3 years. After 3 years, you withdrew $4,360.00 because of losing your job. What is your balance after the withdrawal?
To calculate the balance after the withdrawal, we first need to calculate the total amount in the savings account after 3 years of earning interest.
To calculate the total amount in the savings account after 3 years, we use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (initial deposit)
r = annual interest rate (decimal)
n = number of times that interest is compounded per year
t = number of years the money is invested/borrowed for
Given:
P = $1,763.25
r = 4.5% or 0.045
n = 1 (compounded annually)
t = 3 years
A = $1,763.25(1 + 0.045/1)^(1*3)
A = $1,763.25(1 + 0.045)^3
A = $1,763.25(1.045)^3
A = $1,763.25(1.141630125)
A = $2,010.97365313
After 3 years, the total amount in the savings account is approximately $2,010.97.
Next, we subtract the withdrawal amount of $4,360.00:
$2,010.97 - $4,360.00 = -$2,349.03
Therefore, after the withdrawal, the balance in the savings account is approximately -$2,349.03.
are you sure
Apologies for the miscalculation.
Let's recalculate:
To calculate the total amount in the savings account after 3 years, we use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (initial deposit)
r = annual interest rate (decimal)
n = number of times that interest is compounded per year
t = number of years the money is invested/borrowed for
Given:
P = $1,763.25
r = 4.5% or 0.045
n = 1 (compounded annually)
t = 3 years
A = $1,763.25(1 + 0.045/1)^(1*3)
A = $1,763.25(1 + 0.045)^3
A = $1,763.25(1.045)^3
A = $1,763.25(1.141630125)
A = $2,009.31369188
After 3 years, the total amount in the savings account is approximately $2,009.31.
Next, we subtract the withdrawal amount of $4,360.00:
$2,009.31 - $4,360.00 = -$2,350.69
Therefore, after the withdrawal, the balance in the savings account is approximately -$2,350.69.