Question

3.6.PS-18Question Help0Dakota earned $10.50 in interest in Account A and $15.75 in interest in Account B after 21 months. Ifthe simple interest rate is 4% for Account A and 3% for Account B, which account has the greaterprincipal? Explain.Which account has the greater principal? Select the correct answer below and fill in the answer boxesto complete your choice.O A. Account B because the principal for Account B is $ and the principal for Account A is $•B. Account A because the principal for Account A is $ and the principal for Account B is $OC. Both accounts have the same principal. The principal for both accounts is $10viVi(1)MoreClick to select and enter your answer(s) and then click Check Answer.All parts showingClear AllFinal Check

Answer 1

The formula for simple interest is:

$i=\text{Prt}$

Where

i is the interest earned

P is the principal

r is the rate of interest, in decimal

t is the time, in years

First,

21 months is:

21/12 = 1.75 yr

So, t = 1.75

Account A:

i = 10.50

r = 0.04

t = 1.75

Thus, principal would be:

$\begin{gathered} i=\text{Prt} \\ 10.50=P(0.04)(1.75)_{}_{} \\ 10.50=P(0.07) \\ P=\frac{10.50}{0.07} \\ P=150 \end{gathered}$

Account B:

i = 15.75

r = 0.03

t = 1.75

Thus, principal would be:

$\begin{gathered} i=\text{Prt} \\ 15.75=P(0.03)(1.75) \\ P=\frac{15.75}{(0.03)(1.75)} \\ P=300 \end{gathered}$

The correct answer is A.

Account B because principal for Account B is $300 and the principal for Account A is $150.