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Brianna and Audra are each investing $16,500 at

8% interest. Brianna is earning compound
interest. Audra is earning simple interest. At the
end of 13 years, who will have more, and how
much more?

User Funtime
by
8.2k points

2 Answers

2 votes

Answer:

Brianna will have approximately $2,439.84 more than Audra.

hope it helps u

Explanation:

User Nathan Hinchey
by
8.0k points
5 votes

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: :)

User Dtanabe
by
8.1k points