june has a savings account with an annual simple interest rate of 2.6%. she hopes to gain $6,500 in interest…

june has a savings account with an annual simple interest rate of 2.6%. she hopes to gain $6,500 in interest over a period of eleven years. to accomplish this, june invested $17,801 in the account, but later realized that this was not enough money. to the nearest dollar, how much more money should june have initially invested to reach her goal? a. $6,335 b. $3,715 c. $1,409 d. $4,926 please select the best answer from the choices provided

june has a savings account with an annual simple interest rate of 2.6%. she hopes to gain $6,500 in interest over a period of eleven years. to accomplish this, june invested $17,801 in the account, but later realized that this was not enough money. to the nearest dollar, how much more money should june have initially invested to reach her goal? a. $6,335 b. $3,715 c. $1,409 d. $4,926 please select the best answer from the choices provided

Answer

Explanation:

Step1: Recall simple - interest formula

The simple - interest formula is $I = Prt$, where $I$ is the interest, $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), and $t$ is the time in years. Given $r = 2.6%=0.026$ and $t = 11$ years, and $I = 6500$. We can solve for the required principal $P$.

Step2: Rearrange the formula to solve for $P$

From $I = Prt$, we get $P=\frac{I}{rt}$. Substitute $I = 6500$, $r = 0.026$, and $t = 11$ into the formula: $P=\frac{6500}{0.026\times11}=\frac{6500}{0.286}\approx22727$.

Step3: Calculate the additional amount

The amount June initially invested is $P_1 = 17801$. The additional amount $A$ she should have invested is $A=P - P_1$. So $A = 22727-17801 = 4926$.

Answer:

D. $4,926$