Final answer:
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.