Question

2100 dollars is placed in an account with an annual interest rate of 5%. To the nearest year, how long will it take for the account value to reach 5100 dollars?

Answer 1

To find how long it will take for the account value to reach $5100, we can use the compound interest formula. In this case, it will take approximately 8 years.

Step-by-step explanation:

To find how long it will take for the account value to reach $5100, we need to solve the compound interest formula:

A = P(1 + r/n)^(nt)

Where:

• A is the future value
• P is the principal amount
• r is the annual interest rate (as a decimal)
• n is the number of times the interest is compounded per year
• t is the number of years

Plugging in the given values:

$5100 = $2100(1 + 0.05/1)^(1t)

Simplifying the equation:

2.42857 ≈ 1.05^t

Taking the natural log of both sides:

ln(2.42857) ≈ ln(1.05^t)

Applying the logarithmic properties:

ln(2.42857) ≈ t * ln(1.05)

Solving for t:

t ≈ ln(2.42857) / ln(1.05)

Using a calculator, we find that t ≈ 8.30. Therefore, it will take approximately 8 years for the account value to reach $5100.