Question

two statements were made about each situation below. using the shape tool, circle the incorrect statement and type the statement correctly in the white rectangle. in each situation, assume that no other deposits or withdrawals were made.
1
luis invests $3,500 into an account that earns 4% interest compounded annually for 30 years.
a. luis will earn $4,200 in interest.
b. the balance of luis account will be almost $11,352.
2
anna deposited $2,500 into an account that earns 5% simple interest for 72 months.
a. anna will earn $750 in interest.
b. the balance of annas account will be just over $3,350.
3
ming opened an account earning 2% interest compounded annually for 18 months. mings starting balance was $1,200.
a. ming will earn about $36 in interest.
b. the balance of mings account will be near $1,714.

Explanation:

Situation 1:

Step1: Calculate compound - interest amount

The compound - interest formula is \(A = P(1 + r)^t\), where \(P=\$3500\), \(r = 0.04\), and \(t = 30\).

$$A=3500\times(1 + 0.04)^{30}$$

$$A=3500\times(1.04)^{30}$$

Using a calculator, \((1.04)^{30}\approx3.2434\)

$$A = 3500\times3.2434=\$11351.9\approx\$11352$$

The interest earned \(I=A - P=11352-3500=\$7852\)
So statement A (\(I = \$4200\)) is incorrect.

Situation 2:

Step1: Calculate simple - interest amount

The simple - interest formula is \(I=Prt\). Here, \(P = \$2500\), \(r=0.05\), and \(t=\frac{72}{12}=6\) years.

$$I=2500\times0.05\times6$$

$$I = 2500\times0.3=\$750$$

The balance \(A=P + I=2500 + 750=\$3250\)
So statement B (\(A=\$3350\)) is incorrect.

Situation 3:

Step1: Calculate compound - interest amount

The compound - interest formula is \(A = P(1 + r)^t\). Here, \(P=\$1200\), \(r = 0.02\), and \(t=\frac{18}{12}=1.5\) years.

$$A=1200\times(1 + 0.02)^{1.5}$$

$$A=1200\times1.02^{1.5}$$

$$1.02^{1.5}=\sqrt{1.02^{3}}\approx\sqrt{1.061208}\approx1.03$$

$$A=1200\times1.03=\$1236$$

The interest earned \(I=A - P=1236-1200=\$36\)
So statement B (\(A=\$1714\)) is incorrect.

Answer:

• Situation 1: Incorrect statement is A. The correct interest earned is about \(\$7852\).
• Situation 2: Incorrect statement is B. The balance of Anna's account is \(\$3250\).
• Situation 3: Incorrect statement is B. The balance of Ming's account is near \(\$1236\).