Question

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.

Answer 1

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.