Question

steve deposits $1250 in an account paying 3.4% annual interest compounded continously. how long will it take for the account balance to reach $3150.50​

Answer 1

Answer:

It will take 27.19 years

Step-by-step explanation:

Compound continuous interest can be calculated using the formula:

$A=Pe^{rt}$ , where

• A = the future value of the investment, including interest
• P = the principal investment amount (the initial amount)
• r = the interest rate  of interest in decimal
• t = the time the money is invested for

∵ Steve deposits $1250 in an account

∴ P = 1250

∵ The account paying 3.4% annual interest compounded continuously

∴ r = 3.4%

- Change it to decimal by dividing it by 100

∴ r = 3.4 ÷ 100 = 0.034

∵ The account balance will reach to $3150.5

∴ A = 3150.5

- Substitute The values of A, P and r in the formula above to find t

∵ ​$3150.5=1250e^{0.034t}$

- Divide both sides by 1250

∴  ​$2.5204=e^{0.034t}$

- Insert ㏑ to both sides

∴ ​$ln(2.5204)=ln[e^{0.034t}]$

- Remember that $ln(e^{n})=n$

∵  $ln(e^{0.034t})=0.034t$

∴ ​ln(2.5204) = 0.034t

- Divide both sides by 0.034

∴ 27.18875 = t

∴ t ≅ 27.19

It will take 27.19 years