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koban [17]
3 years ago
10

Olivia invested $2,400 in an account paying an interest rate of 4.6\% compounded continuously. Assuming no deposits or withdrawa

ls are made, how long would it take, to the nearest tenth of a year, for the value of the account to reach $3,550 ?
Mathematics
1 answer:
Vaselesa [24]3 years ago
6 0

Answer:

  8.5

Step-by-step explanation:

For continuous compounding, the account value formula is ...

  A = Pe^(rt)

where P is the invested amount, r is the annual interest rate, and t is the number of years. We want to find t when ...

  3550 = 2400e^(.046t)

  ln(355/240) = 0.046t

  t = ln(355/240)/0.046 ≈ 8.5

It will take 8.5 years for the value to reach $3550.

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