Suppose that the annual interest rate on your checking account is 7.5 percent compounded continuously. In order to have $ 6300 in 7 years, how much should you deposit now? Assume, that the current balance is $ 0.
let the amount be A
A e^(.075(7)) = 6300
A = 6300/(e^.525 = 3726.80
(quickly tell me where that bank is)
To determine how much you should deposit now in order to have $6300 in 7 years with an annual interest rate of 7.5 percent compounded continuously, we can use the formula for continuous compound interest:
A = P * e^(rt)
Where:
A = the final amount ($6300)
P = the initial deposit
e = the base of the natural logarithm (approximately 2.71828)
r = the annual interest rate (7.5 percent or 0.075 as a decimal)
t = the number of years (7)
Let's calculate the initial deposit (P):
6300 = P * e^(0.075 * 7)
First, simplify the exponential term:
6300 = P * e^(0.525)
Next, divide both sides of the equation by e^(0.525):
6300 / e^(0.525) = P
Using a calculator, we can find that e^(0.525) is approximately 1.6891:
6300 / 1.6891 = P
Therefore, the initial deposit should be approximately $3,728.81.
To find out how much should be deposited now in order to have $6300 in 7 years at an annual interest rate of 7.5 percent compounded continuously, we can use the formula for continuous compound interest:
A = P * e^(rt)
Where:
A = the future amount we want to have ($6300)
P = the initial deposit we need to make
e = the base of the natural logarithm, approximately 2.71828
r = the annual interest rate (0.075 in decimal form)
t = the time period in years (7 years in this case)
To find the value of P, we can rearrange the formula:
P = A / e^(rt)
Now let's plug in the values and calculate:
P = 6300 / e^(0.075 * 7)
Using a calculator, we can find that e^(0.075*7) is approximately 2.56903.
P = 6300 / 2.56903
P ≈ $2449.04
Therefore, you should deposit approximately $2449.04 now in order to have $6300 in 7 years at an annual interest rate of 7.5 percent compounded continuously.