suppose you invest $2200 at an annual interest rate of 5.3% compounded continuously. how much will you have in the account after 7 years?
type your answers and then click done.
what is the value of p?
what is the value of r in decimal form?

Question

Accepted Answer

### Sub - question 1: What is the value of $ P $?
# Answer:
$ 2200 $
# Explanation:
## Step1: Identify the principal amount
In the context of continuous compounding interest, $ P $ represents the principal (initial investment). From the problem, the initial investment is $ \$2200 $, so $ P = 2200 $.

### Sub - question 2: What is the value of $ r $ in decimal form?
# Answer:
$ 0.053 $
# Explanation:
## Step1: Convert percentage to decimal
The annual interest rate is given as $ 5.3\% $. To convert a percentage to a decimal, we divide by $ 100 $. So, $ r=\frac{5.3}{100}=0.053 $.

### Sub - question 3: How much will you have in the account after 7 years? (Using the formula for continuous compounding $ A = Pe^{rt} $)
# Answer:
First, we know that $ P = 2200 $, $ r=0.053 $, and $ t = 7 $.
## Step1: Substitute values into the formula
The formula for continuous compounding is $ A=Pe^{rt} $. Substituting the values, we get $ A = 2200\times e^{0.053\times7} $.
## Step2: Calculate the exponent
First, calculate $ 0.053\times7=0.371 $.
## Step3: Calculate $ e^{0.371} $
Using a calculator, $ e^{0.371}\approx1.450 $ (more accurately, $ e^{0.371}\approx e^{0.37 + 0.001}=e^{0.37}\times e^{0.001}\approx1.447 + 0.001\times1.447\approx1.4484$, but using a calculator directly $ e^{0.371}\approx1.450$).
## Step4: Calculate $ A $
Then, $ A=2200\times1.450 = 3190 $ (more accurately, $ 2200\times e^{0.371}\approx2200\times1.45027\approx3190.59 $). So, approximately $ \$3190.6 $ (or more precisely around $ \$3190.59 $).

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QUESTION IMAGE

Question

Explanation:

Sub - question 1: What is the value of \( P \)?

Step1: Identify the principal amount

Sub - question 2: What is the value of \( r \) in decimal form?

Step1: Convert percentage to decimal

Sub - question 3: How much will you have in the account after 7 years? (Using the formula for continuous compounding \( A = Pe^{rt} \))

Answer: