Answer: To compare the final amounts, we need to calculate the compound interest for Brianna and the simple interest for Audra.
For compound interest, the formula to calculate the future value is:
A = P(1 + r/n)^(nt)
Where:
A = the future value/amount
P = the principal amount (initial investment)
r = the annual interest rate (as a decimal)
n = the number of times that interest is compounded per year
t = the number of years
For Brianna:
P = $16,500
r = 8% = 0.08
n = 1 (compounded annually)
t = 13 years
A = 16500(1 + 0.08/1)^(1*13)
A = 16500(1.08)^13
A ≈ $42,159.84
After 13 years, Brianna will have approximately $42,159.84.
For simple interest, the formula to calculate the future value is:
A = P(1 + rt)
Where:
A = the future value/amount
P = the principal amount (initial investment)
r = the annual interest rate (as a decimal)
t = the number of years
For Audra:
P = $16,500
r = 8% = 0.08
t = 13 years
A = 16500(1 + 0.08*13)
A = 16500(1 + 1.04)
A ≈ $39,720
After 13 years, Audra will have approximately $39,720.
To determine who will have more and by how much, we subtract Audra's amount from Brianna's amount:
Difference = Brianna's amount - Audra's amount
Difference = $42,159.84 - $39,720
Difference ≈ $2,439.84
Therefore, at the end of 13 years, Brianna will have approximately $2,439.84 more than Audra.
Step-by-step explanation: :)