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Anna35 [415]
3 years ago
11

steve deposits $1250 in an account paying 3.4% annual interest compounded continously. how long will it take for the account bal

ance to reach $3150.50​
Mathematics
1 answer:
Tomtit [17]3 years ago
3 0

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

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