Final answer:
The time period in years is calculated by rearranging the simple interest formula and substituting the given values to find that $16,000 was deposited for a period of 50 months to earn $4,000 at a 6% interest rate.
Step-by-step explanation:
To find the time period in years that $16,000 was deposited in a savings account to earn $4,000 in interest at a simple interest rate of 6%, we can rearrange the simple interest formula I = Prt to solve for t. This formula relates the interest earned (I), the principal amount deposited (P), the rate of interest (r), and the time the money is invested (t).
Using the information provided, the principal P is $16,000, the interest I is $4,000, and the rate r is 6% or 0.06 in decimal form. Substituting these values into the formula leads to:
4000 = 16000 × 0.06 × t
Dividing both sides by (16000 × 0.06) gives:
t = 4000 / (16000 × 0.06)
t = 4000 / 960
t = 4.1667 years
Since we need to find the time in months, we can convert years to months by multiplying by 12:
t in months = 4.1667 × 12
t in months = 50 months
Therefore, the answer is option (d) 50 months.