Question

Daniel wants to open an account to purchase a new computer. He was able to put $750 into an account that pays him 8.5% interest. The cost of the computer he wants is $1,150.00. How long will he have to wait to withdraw the money?

Answer 1

Answer:

Daniel has to wait around 5.24 years to withdraw the money.

Step-by-step explanation:

We are given that Daniel wants to open an account to purchase a new computer. He was able to put $750 into an account that pays him 8.5% interest. The cost of the computer he wants is $1,150.00.

Let the Principal sum of money be represented by 'P'.

The rate of interest be represented by 'R'.

The time period be represented by 'T'.

The final amount of money be represented by 'A'.

Assuming the interest given is compound interest.

So, the formula for calculating the amount of money is given by;

                          $\text{A} = \text{P} \times (1-\text{R})^{\text{T}}$

Here, A = $1,150, P = $750, R = 8.5% and let the time he have to wait to withdraw the money be 'n'.

So, putting these values in the above formula we get;

$\text{A} = \text{P} \times (1+\text{R})^{\text{T}}$

$\text{\ 1,150} = \text{750} \times (1+\text{0.085})^{\text{n}}$

$(1+\text{0.085})^{\text{n}} = \frac{\ 1,150}{\ 750}$

$(1+\text{0.085})^{\text{n}} = 1.533$

Taking log on both sides;

$\text{n} \times ln(1+\text{0.085}) = ln(1.533)$

$n = \frac{ ln(1.533)}{ ln(1.085)}$

n = 5.24 years

Hence, he has to wait around 5.24 years to withdraw the money.