Answer:
It will take 27.19 years
Step-by-step explanation:
Compound continuous interest can be calculated using the formula:
, 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
∵
- 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