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$6746 is deposited into a savings account at 5% interest, compounded quarterly. To the nearest year, how long will it take for the account balance to reach $1,000,000?

Respuesta :

nkirotedoreen46

Answer:

101 years

Step-by-step explanation:

From the question we are given;

  • Amount deposited (principal) $6746
  • Rate of interest 5%
  • Amount accrued is $ 1,000,000

We are required for the amount invested to accrue to the amount given;

We are going to use the compound interest formula;

[tex]A = P (1 + \frac{R}{100})^n[/tex], Where A is the amount accrued, P is the principal amount, R is the rate of interest.

R = 5 ÷ 4

  = 1.25 % ( compounded quarterly)

Therefore;

[tex]1000,000=6746(1+\frac{1.25}{100})^n[/tex]

[tex]148.236=(1.0125)^n[/tex]

Introducing logarithms on both sides

[tex]log148.236=log(1.0125)^n\\log148.236=nlog(1.0125)\\n=\frac{log148.236}{log(1.0125)} \\ = 402.398[/tex]

But, 1 year = 4 quarters

Therefore;

Number of years = 402.398 ÷ 4

                             =100.6 years

                            = 101 years

Thus, it will take approximately 101 years

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