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Zoe invested $780 in an account paying an interest rate of 5.7% compounded daily. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach $1,230?

Respuesta :

mhanifa

Answer:

  • 8 years

Step-by-step explanation:

Given

  • Investment P = $780
  • Interest rate r = 5.7% = 0.057 annually compounded daily
  • Number of compounds n = 365
  • Final amount A = $1230
  • Time t = x

Required formula

  • A = P(1 + r/n)ⁿˣ

Substitute values and solve for x

  • 1230 = 780(1 + 0.057/365)³⁶⁵ˣ
  • 1.05865ˣ = 1230/780
  • 1.05865ˣ = 1.57692
  • x = log 1.57692 / log 1.05865
  • x = 8 years

Answer:

8 years

Step-by-step explanation:Given

Investment P = $780

Interest rate r = 5.7% = 0.057 annually compounded daily

Number of compounds n = 365

Final amount A = $1230

Time t = x

Required formula

A = P(1 + r/n)ⁿˣ

Substitute values and solve for x

1230 = 780(1 + 0.057/365)³⁶⁵ˣ

1.05865ˣ = 1230/780

1.05865ˣ = 1.57692

x = log 1.57692 / log 1.05865

x = 8 years

 

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