Question

1. Calculate the present worth of 9 uniform payments of $10,800 that begin 1 year from now at an interest rate of 5% per year. The present worth is $________________.

2. What is the equivalent annual cost in years 1 through 9 of a contract that has a first cost of $78,000 in year 0 and annual costs of $20,000 in years 3 through 9 ? Use an interest rate of 14% per year. The equivalent annual cost is determined to be $___________________.

Answer 1

To calculate the present worth of 9 uniform payments starting 1 year from now at an interest rate of 5% per year, use the formula for Present Value of an Annuity. The present worth of these payments is $78,732.72.

Step-by-step explanation:

To calculate the present worth of 9 uniform payments, we can use the formula for Present Value of an Annuity.

Present Worth = (Payment / (1 + interest rate)) + (Payment / (1 + interest rate)^2) + ... + (Payment / (1 + interest rate)^n), where

Payment = $10,800

Interest rate = 5%

n = 9

Substituting the values into the formula, we can calculate the present worth:

Present Worth = ($10,800 / (1 + 0.05)) + ($10,800 / (1 + 0.05)^2) + ... + ($10,800 / (1 + 0.05)^9)

Using a calculator or spreadsheet, we find that the present worth of 9 uniform payments of $10,800, starting 1 year from now at an interest rate of 5% per year, is $78,732.72.