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Lady bird [3.3K]
2 years ago
11

Serenity invested $2,400 in an account paying an interest rate of 3.4% compounded

Mathematics
1 answer:
Alisiya [41]2 years ago
8 0

Answer:

It would take 5.9 years to the nearest tenth of a year

Step-by-step explanation:

The formula of the compound continuously interest is A = Pe^{rt} , where

  • A is the value of the account in t years
  • P is the principal initially invested
  • e is the base of a natural logarithm
  • r is the rate of interest in decimal

∵ Serenity invested $2,400 in an account

∴ P = 2400

∵ The account paying an interest rate of 3.4%, compounded continuously

∴ r = 3.4% ⇒ divide it by 100 to change it to decimal

∴ r = 3.4 ÷ 100 = 0.034

∵ The value of the account reached to $2,930

∴ A = 2930

→ Substitute these values in the formula above to find t

∵ 2930 = 2400e^{0.034t}

→ Divide both sides by 2400

∴ \frac{293}{240} = e^{0.034t}

→ Insert ㏑ in both sides

∴ ㏑(\frac{293}{240}) = ㏑(e^{0.034t})

→ Remember ㏑(e^{n}) = n

∴ ㏑(\frac{293}{240}) = 0.034t

→ Divide both sides by 0.034 to find t

∴ 5.868637814 = t

→ Round it to the nearest tenth of a year

∴ t = 5.9 years

∴ It would take 5.9 years to the nearest tenth of a year

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