Determine how much money will be in a savings account if the initial deposit was $1000 and the interest rate is 4% compounded continuously for 15 years, 6 months.
P = Po*e^rt.
Po = $1000.
rt = 0.04/yr * 15.5yrs = 0.62
P = 1000*e^0.62 = $1858.93.
To determine the amount of money in the savings account after 15 years and 6 months with continuous compounding, we can use the formula:
A = P * e^(rt)
Where:
A = the final amount in the savings account
P = the initial deposit
e = Euler's number (approximately 2.71828)
r = interest rate (expressed as a decimal)
t = time in years
Given:
P = $1000
r = 4% = 0.04 (as a decimal)
t = 15.5 years
Plugging in these values, we can calculate the final amount:
A = $1000 * e^(0.04 * 15.5)
Now, let's calculate the result step-by-step:
Step 1: Multiply the interest rate (0.04) by the time in years (15.5):
0.04 * 15.5 = 0.62
Step 2: Raise Euler's number (approximately 2.71828) to the power calculated in step 1:
e^0.62 ≈ 1.85913
Step 3: Multiply the initial deposit ($1000) by the result from step 2:
$1000 * 1.85913 ≈ $1859.13
Therefore, there will be approximately $1859.13 in the savings account after 15 years and 6 months with continuous compounding.
To determine the amount of money in a savings account with continuous compounding, we can use the formula:
A = P * e^(rt),
where:
A = the final amount of money in the account
P = the initial deposit
e = the base of the natural logarithm (approximately 2.71828)
r = the interest rate (in decimal form)
t = the time period (in this case, measured in years)
Let's calculate it step by step:
1. Convert the interest rate from a percentage to a decimal:
r = 4% = 4/100 = 0.04.
2. Convert the time period to years:
t = 15 years + 0.5 years = 15.5 years.
3. Substitute the values into the continuous compounding formula:
A = $1000 * e^(0.04 * 15.5).
4. Calculate the value of e^(0.04 * 15.5) using a calculator or math software:
e^(0.04 * 15.5) ≈ 2.71828^(0.62) ≈ 2.132.
5. Multiply the initial deposit by the calculated value:
A ≈ $1000 * 2.132 ≈ $2132.
Therefore, the final amount of money in the savings account after 15 years and 6 months, with an initial deposit of $1000 and a continuous interest rate of 4%, will be approximately $2132.