138k views
12 votes
Ernesto has $20 in an account. The interest rate is 10% compounded annually.

To the nearest cent, how much interest will he earn in 1 year?
Use the formula B=p(1+r)t, where B is the balance (final amount), p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.

1 Answer

12 votes

Final answer:

Ernesto needs to deposit approximately $3,855.43 into a bank account paying 10% interest compounded annually to have $10,000 in ten years.

Step-by-step explanation:

To calculate the amount Ernesto needs to deposit now to have $10,000 in ten years with an interest rate of 10% compounded annually, we need to rearrange the compound interest formula:

B = p(1 + r)t

where:

  • B is the balance (final amount)
  • p is the principal (starting amount)
  • r is the interest rate expressed as a decimal
  • t is the time in years

We know B = $10,000, r = 0.10 (which is 10% as a decimal), and t = 10.

To find p, we rearrange the formula to solve for p:

p = B / (1 + r)t

Substitute the known values in:

p = $10,000 / (1 + 0.10)10

p = $10,000 / (1.10)10

p = $10,000 / 2.59374

p ≈ $3,855.43

Ernesto needs to deposit approximately $3,855.43 to have $10,000 in ten years at a 10% annual compound interest rate.

User Fabian Zeindl
by
7.6k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.