Question

Compute the present value of $9,000 paid in four years using the following discount rates: 4 percent in year 1, 5 percent in year 2, 4 percent in year 3, and 3 percent in year 4.

Answer 1

The sum would amount to $10,527.75 after the end of 4 years.

Explanation:

The Problem pertains to compounding interest with varying rates over the years. Our approach to solve the problem would be in a chronological fashion starting with the 1st year

Principal- $ 9000

Rate interest= 4%

Time period would be 1 year since the interest are considered for successive years.

We know the formulae- Amount= Principal (1+rate/100) ⁿ

Where “n”= time period= 1 in all cases

⇒Amount after 1st year at 4% rate= 9000(1+4/100)

9000*104/100= $ 9360

This amount would serve as Principal for 2nd year

⇒Hence, Amount for 2nd year at 5% rate= 9360(1+5/100)

9000*105/100= $ 9828

⇒Similarly, Amount for 3rd year at 4% rate= 9828(1+4/100)

=9828*104/100= $ 10,221.12

⇒Amount for the last year at 3% rate= 10,221.12(1+3/100)

=10,221.12*103/100= $ 10527.75

Hence the present value of the amount is $ 10527.75 after the end of 4 years.