Question

8000$ is invested in an account the yields 6% interest per year. After how many years will the account worth 13709.60$ if the interest is compounded monthly?

Answer 1

Answer:

After 9 years the account will be worth 13709.60$

Step-by-step explanation:

We are given the following in the question:

We are given the following in the question:

P = $8000

r = 6% = 0.046

n = 12

The compound interest is given by:

$A = p\bigg(1+\dfrac{r}{n}\bigg)^{nt}$

where A is the amount, p is the principal, r is the interest rate, t is the time in years.

Putting the values, we get,

$13709.60 = 8000\bigg(1+\dfrac{0.06}{12}\bigg)^{12t}\\\\\dfrac{13709.60}{8000} = \bigg(1+\dfrac{0.06}{12}\bigg)^{12t}\\\\\Rightarrow 1.7137 = (1.005)^{12t}\\\Rightarrow t \approx 9$

Thus, after 9 years the account will be worth 13709.60$

Answer 2

Answer: It will take 9 years to get the account worth $13709.60

Step-by-step explanation:

Since we have given that

Sum = $8000

Rate of interest = 6%

Amount = $13709.60

According to question, we get that

$A=P(1+\dfrac{r}{n})^{nt}\\\\13709.60=8000(1+\dfrac{0.06}{12})^{12t}\\\\\dfrac{13709.60}{8000}=(1+\dfrac{0.06}{12})^{12t}\\\\1.7137=(1+0.005)^{12t}\\\\1.7137=1.005^{12t}\\\\t=9\ yrs$

Hence, it will take 9 years to get the account worth $13709.60