futuresecure bank claims that by depositing $5,000 in a savings account with a 7% annual interest rate…

futuresecure bank claims that by depositing $5,000 in a savings account with a 7% annual interest rate compounded quarterly, the amount will grow to $10,000 in 7 years without any additional deposits. is this claim true? true. the amount will grow to exactly $10,000 in 7 years at a 7% interest rate. false. the amount will not reach $10,000 in 7 years at a 7% interest rate. false. the amount will exceed $10,000 in 7 years at a 7% interest rate. false. the amount will not reach $8,000 in 7 years at a 7% interest rate.

futuresecure bank claims that by depositing $5,000 in a savings account with a 7% annual interest rate compounded quarterly, the amount will grow to $10,000 in 7 years without any additional deposits. is this claim true? true. the amount will grow to exactly $10,000 in 7 years at a 7% interest rate. false. the amount will not reach $10,000 in 7 years at a 7% interest rate. false. the amount will exceed $10,000 in 7 years at a 7% interest rate. false. the amount will not reach $8,000 in 7 years at a 7% interest rate.

Answer

Answer:

B. False. The amount will not reach $10,000 in 7 years at a 7% interest rate.

Explanation:

Step1: Identify compound - interest formula

The compound - interest formula is $A = P(1+\frac{r}{n})^{nt}$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal), $n$ is the number of times interest is compounded per year, and $t$ is the number of years.

Step2: Convert values to appropriate form

Given $P = 5000$, $r=0.07$, $n = 4$ (compounded quarterly), and $t = 7$.

Step3: Substitute values into formula

$A=5000(1 +\frac{0.07}{4})^{4\times7}=5000(1 + 0.0175)^{28}$.

Step4: Calculate $(1 + 0.0175)^{28}$

$(1 + 0.0175)^{28}\approx1.6165$.

Step5: Calculate $A$

$A = 5000\times1.6165=8082.5$. Since $8082.5<10000$, the claim is false.