If $1500 is invested at an interest rate of 3.5% per year, compounded continuously, find the value of the investment after 3 and 6 years.
What formula would i use?
(1.035)^years * 1500
To find the value of an investment compounded continuously, you can use the formula:
A = P * e^(rt)
where:
A = the final amount (value of the investment)
P = the initial principal (investment amount)
e = the mathematical constant approximately equal to 2.71828
r = the interest rate per year (as a decimal)
t = the time in years
Using this formula, you can calculate the value of the investment after 3 and 6 years.
To find the value of an investment after a certain period of time with continuous compounding, you can use the formula:
A = P * e^(rt)
Where:
A is the final amount (value of the investment)
P is the initial principal (amount invested)
e is the base of the natural logarithm (approximately 2.71828)
r is the interest rate per time period (in this case, per year)
t is the time period in years
In your case, the initial principal (P) is $1500, the interest rate per year (r) is 3.5% or 0.035 (in decimal form), and the time period (t) is 3 and 6 years respectively.
Let's calculate the value of the investment after 3 years:
A = $1500 * e^(0.035 * 3)
To calculate this value, you can substitute the values into a scientific calculator or use online calculators that have an exponential function. The final result will give you the value of the investment after 3 years. Similarly, you can calculate the value after 6 years.