Find the present value of $100,000 if interest is paid at a rate of 8% per year, compounded monthly, for 5 years.
PV = 100000( 1 + .08/12)^-60
= 100000( 1.0066666..)^-60
= ...
Define a new function, h(x), which shifts g(x) to the left by 2 units and down 3 units, and also makes g(x) increase faster vertically by some factor (your choice).
What is the equation for h(x)?
A ball is thrown upward with an initial velocity of 48 ft/sec from a height 640 ft. Its height h, in feet, after t seconds is given by h(t)=-16t^2+48t+640. After how long will the ball reach the ground?
To find the present value of an amount given a certain interest rate and time period, we can use the formula for calculating the present value of a future sum of money:
Present Value = Future Value / (1 + r/n)^(n*t)
Where:
- Future Value is the amount you want to calculate the present value for ($100,000 in this case)
- r is the annual interest rate (8% or 0.08 in decimal form)
- n is the number of times interest is compounded per year (compounded monthly, so 12)
- t is the number of years (5 in this case)
Plugging in the values into the formula:
Present Value = 100000 / (1 + 0.08/12)^(12*5)
Calculating inside the parentheses first:
Present Value = 100000 / (1 + 0.0066667)^(60)
Using a calculator or spreadsheet software, we can calculate the present value:
Present Value ≈ $67,567.75
Therefore, the present value of $100,000, with interest paid at a rate of 8% per year, compounded monthly, for 5 years, is approximately $67,567.75.