3) Suppose you deposit $10,000 in a savings account that pays interest at an annual rate of 5% compounded quarterly. How many years will it take for the balance in your savings account to reach
$12,000?

9514 1404 393

  3.67 years

Step-by-step explanation:

The amount is found using the compound interest formula.

  A = P(1 +r/n)^(nt)

for principal P invested at annual rate r compounded n times per year for t years.

We can solve this for t:

  A/P = (1 +r/n)^(nt) . . . . divide by P

  log(A/P) = (nt)log(1 +r/n) . . . . take the logarithm

  t = log(A/P)/(n·log(1 +r/n)) . . . . divide by the coefficient of t

Filling in the given values, we find ...

  t = log(12000/10000)/(4·log(1 +0.05/4)) ≈ 3.6692

It will take about 3.67 years for the balance to reach $12,000.

the answer is 3.67 years

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step-by-step explanation:

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