what is the present value of 1000 paid at the end of each of the next 100 years if the interest rate is 7% per year
PV = 1000(1 - 1.07^-100)/.07
= .... (you do the button-pushing)
To calculate the present value of a future payment, we need to discount the future cash flows back to the present using a discount factor. The discount factor is determined by the interest rate and the time period. In this case, we have $1,000 paid at the end of each of the next 100 years with an interest rate of 7% per year.
To calculate the present value, we will use the formula for the present value of an annuity:
Present Value = Cash Flow / (1 + r)^n
where:
- Cash Flow is the amount of money received each period (in this case, $1,000)
- r is the interest rate per period (7% or 0.07 in decimal form)
- n is the number of periods (100 years)
Let's plug in the values into the formula:
Present Value = $1,000 / (1 + 0.07)^100
To calculate this, you can use a calculator or a spreadsheet program. The result will be the present value of receiving $1,000 at the end of each year for 100 years with an interest rate of 7% per year.
To calculate the present value of a series of future payments, we can use the formula for calculating the present value of an annuity. The formula for the present value of an annuity is:
PV = A * [1 - (1 + r)^(-n)] / r
Where:
PV = Present value
A = Amount of each payment
r = Interest rate per period
n = Number of periods
In this case, we are given an interest rate of 7% per year and 100 payments of $1000.
Using the formula, let's calculate the present value:
PV = 1000 * [1 - (1 + 0.07)^(-100)] / 0.07
Now, let's calculate it step-by-step:
Step 1: Calculate the value inside the square brackets.
(1 + 0.07)^(-100) ≈ 0.024097951
Step 2: Subtract the value from 1.
1 - 0.024097951 = 0.975902049
Step 3: Divide this result by the interest rate.
0.975902049 / 0.07 ≈ 13.941885
Step 4: Multiply the above result by the amount of each payment.
13.941885 * 1000 = 13,941.885
Therefore, the present value of receiving $1000 at the end of each of the next 100 years, with an interest rate of 7% per year, is approximately $13,941.89.