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118. Sami opens an account and deposits $100 into it at the end of each month. The account earns 2% per year compounded monthly. Let Sn denote the amount of money in her account at the end of n months (just after she makes a deposit). For example, S1 = 100 and S2 = 100(1 + 0.02 /12)+100
d. When will Sami have at least $5,000 in her account? Show work to support your answer.

Respuesta :

Limosa

Answer:

The answer = 48.07 approx.

Step-by-step explanation:

b)

5000 = 100 (1 -( 1+ \frac{0.02}{12} )^n) / 1 - ( 1 + \frac{0.02}{12})

50 (- \frac{0.02}{12}) = 1 - ( 1 + \frac{0.02}{12} )^n

\frac{13}{12} = 1 + \frac{0.02}{12})^n

n = log(\frac{13}{12}) = log(1 + \frac{0.02}{12})^n

n = log(\frac{13}{12}) \ log(1 + \frac{0.02}{12})^n

The answer = 48.07 approx.

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