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

It will take 27.19 years

Step-by-step explanation:

Compound continuous interest can be calculated using the formula:

, where

∵ 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

∵

- Divide both sides by 1250

∴  

- Insert ㏑ to both sides

∴

- Remember that

∵  

∴ 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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