A bank deposit paying simple interest at the rate of 4%/year grew to a sum of $1,900 in 11 months. Find the principal. Round your answers to nearest integer.
A) The principal is $1,812.
B) The principal is $1,889.
C) The principal is $1,896.
D) The principal is $4,400.
E) The principal is $1,833.

Question

A bank deposit paying simple interest at the rate of 4%/year grew to a sum of $1,900 in 11 months. Find the principal. Round your answers to nearest integer. ​
A) The principal is $1,812.
B) The principal is $1,889.
C) The principal is $1,896.
D) The principal is $4,400.
E) The principal is $1,833.

Quizplus · Accepted Answer

The formula for simple interest is $I = P \times r \times t$, where $I$ is the interest earned, $P$ is the principal amount, $r$ is the annual interest rate, and $t$ is the time the money is invested for in years. Given that the total amount after 11 months is $1,900 and the interest rate is 4% per year, we first convert 11 months into years ($\frac{11}{12}$ years). Let $P$ be the principal. The interest earned can be calculated as $1900 - P$. Setting up the equation:$$1900 - P = P \times 0.04 \times \frac{11}{12}$$Solving for $P$ gives us the principal amount. Rearranging and solving the equation:$$P = \frac{1900}{1 + (0.04 \times \frac{11}{12})}$$$$P \approx 1833$$Therefore, the principal is approximately $1,833, rounded to the nearest integer.

A Bank Deposit Paying Simple Interest at the Rate of 4%/year