Question

Natalie has $5000 and decides to put her money in the bank in an account that has a 10% interest rate that is compounded continuously.
What type of exponential model is Natalie’s situation?
Write the model equation for Natalie’s situation
How much money will Natalie have after 2 years?
How much money will Natalie have after 10 years?

Answer 1

Step-by-step explanation:

• Natalie has $5000

• She decides to put her money in the bank in an account that has a 10% interest rate that is compounded continuously.

Part a) What type of exponential model is Natalie’s situation?

Answer:

As Natalie's situation implies

• continuous compounding. So, instead of computing interest on a finite number of time periods, for instance monthly or yearly, continuous compounding computes interest assuming constant compounding over an infinite number of periods.

So, it requires the more generalized version of the principal calculation formula such as:

$P\left(t\right)=P_0\times \left[1+\left(i\:/\:n\right)\right]^{\left(n\:\times \:\:t\right)}$

or

$P\left(t\right)=P_0\times \left[1+\left(\frac{i}{n}\:\right)\right]^{\left(n\:\times \:\:t\right)}$

Here,

$i$ = interest rate

= number of compounding periods

$t$ = time period in years

Part b) Write the model equation for Natalie’s situation?

For continuous compounding the number of compounding periods, $n$, becomes infinitely large.

Therefore, the formula as we discussed above would become:

                                        $P\left(t\right)=P_0\times e^{\left(i\:\times \:t\right)}$

Part c) How much money will Natalie have after 2 years?

Using the formula

                            $P\left(t\right)=P_0\times e^{\left(i\:\times \:t\right)}$

$₂ $=\:6107.02$ $

So, Natalie will have $\:6107.02$ $ after 2 years.

Part d) How much money will Natalie have after 2 years?

Using the formula

                            $P\left(t\right)=P_0\times e^{\left(i\:\times \:t\right)}$

$₁₀ $=13.597.50$ $

So, Natalie will have $13.597.50$ $ after 10 years.

Keywords: word problem, interest

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