Question

SHORT ANSWER 22. A workshop designed to retrain workers 55 years of age and older who have lost their jobs is proposed. Suppose the workshop will increase the income of each participant by $1,000 per year for a period of 10 years. Calculate the PV of the increased income per participant with each of the following discount rates: 1%,3%, 5% and 10%.

Answer 1

Calculate the pv of the increased income for participant with each of the following discount rates: 0%, 1%, 3%, 5%, & 10% * pv formula use to find the pv of 10 cash-flows of 1000 each with following interest rates. 0% $ 10,000 1% $ 9,471.3 3% $ 8,530.2 5% $ 7,721.73 10% $ 6,144.57

Answer 2

SOLUTION :

1. Discount rate is 1% :

PV is given by the following formula :

PV = A((1+r)^n - 1) / (r (1 + r)^n)

Where,

r = 1% = 0.01

=> 1+ r = 1.01 

A = annuity (income) = 1000 ($)

n = period = 10 years.

So,

PV = 1000(1.01^10 - 1) / (0.01 * 1.01^10) = 9471.30 ($) (ANSWER).

2. Discount rate is 3% :

PV is given by the following formula :

PV = A((1+r)^n - 1) / (r (1 + r)^n)

Where,

r = 3% = 0.03

=> 1+ r = 1.03 

A = annuity (income) = 1000 ($)

n = period = 10 years.

So,

PV = 1000(1.03^10 - 1) / (0.03 * 1.03^10) = 8530.20 ($) (ANSWER).

3. Discount rate is 5% :

PV is given by the following formula :

PV = A((1+r)^n - 1) / (r (1 + r)^n)

Where,

r = 5% = 0.05

=> 1+ r = 1.05

A = annuity (income) = 1000 ($)

n = period = 10 years.

So,

PV = 1000(1.05^10 - 1) / (0.05 * 1.05^10) = 7721.73 ($) (ANSWER).

4. Discount rate is 10% :

PV is given by the following formula :

PV = A((1+r)^n - 1) / (r (1 + r)^n)

Where,

r = 10% = 0.1

=> 1+ r = 1.1 

A = annuity (income) = 1000 ($)

n = period = 10 years.

So,

PV = 1000(1.1^10 - 1) / (0.1 * 1.1^10) = 6144.57 ($) (ANSWER).