Answer :
To solve the problem of finding the future value of Jamar's investment with continuous compounding, use the continuous compounding formula:
[tex]\[ A = P_0 \cdot e^{r \cdot t} \][/tex]
Here's a step-by-step explanation:
1. Initial Investment (Principal), [tex]\( P_0 \)[/tex]:
- This is the initial amount Jamar invested, which is [tex]$3700.
2. Interest Rate, \( r \):
- The interest rate for Jamar's investment is 3.375% per year.
- Convert the percentage to a decimal by dividing by 100, so \( r = 0.03375 \).
3. Time, \( t \):
- The time period for the investment is 20 years.
4. Exponential Growth Factor, \( e^{r \cdot t} \):
- Calculate the exponent: \( r \cdot t = 0.03375 \times 20 = 0.675 \).
5. Calculate the Future Value, \( A \):
- Using the continuous compounding formula, plug in the values:
- \( A = 3700 \times e^{0.675} \).
6. Result:
- After performing the calculation, the future value of Jamar's investment is approximately $[/tex]7266.92.
This is the amount Jamar will have after 20 years with continuous compounding at an interest rate of 3.375% per annum.
[tex]\[ A = P_0 \cdot e^{r \cdot t} \][/tex]
Here's a step-by-step explanation:
1. Initial Investment (Principal), [tex]\( P_0 \)[/tex]:
- This is the initial amount Jamar invested, which is [tex]$3700.
2. Interest Rate, \( r \):
- The interest rate for Jamar's investment is 3.375% per year.
- Convert the percentage to a decimal by dividing by 100, so \( r = 0.03375 \).
3. Time, \( t \):
- The time period for the investment is 20 years.
4. Exponential Growth Factor, \( e^{r \cdot t} \):
- Calculate the exponent: \( r \cdot t = 0.03375 \times 20 = 0.675 \).
5. Calculate the Future Value, \( A \):
- Using the continuous compounding formula, plug in the values:
- \( A = 3700 \times e^{0.675} \).
6. Result:
- After performing the calculation, the future value of Jamar's investment is approximately $[/tex]7266.92.
This is the amount Jamar will have after 20 years with continuous compounding at an interest rate of 3.375% per annum.
