the following investments require table factors for periods beyond the table, create the new table factors AND present value $31,000 (compound amount) time period is 50 years nominal rate is 5% and interest compounded annually thanks
To calculate the present value of $31,000 after 50 years, we will need to use the formula for compound interest:
PV = A / (1 + r)^n
Where:
PV = Present Value
A = Future value or compound amount
r = Interest rate per period
n = Number of periods
In this case, the compound amount (A) is $31,000, the interest rate (r) is 5% or 0.05, and the number of periods (n) is 50 years.
Substituting these values into the formula, we get:
PV = $31,000 / (1 + 0.05)^50
To calculate this expression, you can use a scientific calculator or spreadsheet software. However, since you mentioned creating new table factors, I assume you want to calculate it using table factors.
Table factors are values that help you find the present value by looking up the corresponding factor in the table for a given interest rate and number of periods. However, in this case, the table factors for a period of 50 years may not be readily available.
To create the new table factors, you can use the formula for calculating the table factor:
Factor = 1 / (1 + r)^n
For each year, you can calculate the table factor using this formula:
Year 0: Factor0 = 1 / (1 + 0.05)^0 = 1
Year 1: Factor1 = 1 / (1 + 0.05)^1
Year 2: Factor2 = 1 / (1 + 0.05)^2
...
Year 49: Factor49 = 1 / (1 + 0.05)^49
Year 50: Factor50 = 1 / (1 + 0.05)^50
Once you have calculated these table factors, you can multiply the compound amount ($31,000) by the factor for the corresponding number of years to find the present value.
For example, to calculate the present value after 50 years using the table factors, you would do:
PV = $31,000 * Factor50
Remember to round the result to an appropriate number of decimal places, depending on the accuracy required.