Answer: To calculate the amount Patti will have in the account after five years, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the final amount in the account after t years
P = the initial principal (the amount deposited at the end of each quarter)
r = the annual interest rate (in decimal form)
n = the number of times interest is compounded per year
t = the number of years
Given:
P = $1,600 (deposited at the end of each quarter)
r = 8% = 0.08 (converted to decimal form)
n = 4 (compounded quarterly)
t = 5 years
Now, plug in the values into the formula:
A = 1600(1 + 0.08/4)^(4*5)
A = 1600(1 + 0.02)^(20)
A = 1600(1.02)^20
Using a calculator, calculate the value of (1.02)^20:
(1.02)^20 ≈ 1.485946
Now, multiply by $1600:
A ≈ 1600 * 1.485946 ≈ $2,377.51
So, Patti will have approximately $2,377.51 in the account after five years.
None of the multiple-choice options match the calculated value exactly. The closest option is $40,476, but the correct value is $2,377.51.