Chapter 21: Savings Models

Transcription

1 October 18, 2013

2 Last Time A Model for Saving Present Value and Inflation

3 Problems Question 1: Suppose that you want to save up $2000 for a semester abroad two years from now. How much do you have to put away at the end of each month in a savings account that earns 2 % interest compounded monthly? Question 2: A colleague feels that he will need $1 million in savings to afford to retire at age 65 and still maintain his current standard of living. Younger colleague, age 30, decides to begin savings for retirement based on that advice. How much does the younger colleague need to save per month to have $ 1 million at retirement if the fund earns a steady 3% annual interest compounded monthly? Question 3: Suppose you start saving for retirement at age 45. How much do you have to save per month, with a steady return of 6% compounded monthly, to accumulate $250,000 by age 65?

4 Answers Question 1: Suppose that you want to save up $2000 for a semester abroad two years from now. How much do you have to put away at the end of each month in a savings account that earns 2 % interest compounded monthly? Payment Formula [ ] i d = A (1 + i) n 1 [ = A r/m (1 + r m )mt 1 ] Answer: [ ].02/12 d = 2000 (1 + (.02/12)) 24 1 = 81.75

5 Answers Question 2: A colleague feels that he will need $1 million in savings to afford to retire at age 65 and still maintain his current standard of living. Younger colleague, age 30, decides to begin savings for retirement based on that advice. How much does the younger colleague need to save per month to have $ 1 million at retirement if the fund earns a steady 3% annual interest compounded monthly? Answer: [ ].03/12 d = (1 + (.03/12)) 35(12) = If he started at age 45: [ ].03/12 d = (1 + (.03/12)) 20(12) =

6 Answers Question 3: Suppose you start saving for retirement at age 45. How much do you have to save per month, with a steady return of 6% compounded monthly, to accumulate $250,000 by age 65? Answer: [ ].06/12 d = (1 + (.06/12)) 20(12) =

7 Problems Question 4: What is the present value of $10,000, 4 years from now, at an APY of 5%? Question 5: What is the present value of $15,000, 10 years from now, at an APY of 3%? Question 6: Suppose that inflation proceeds at a constant rate of 2% per year from mid through mid a) Find the cost in mid-2015 of a basket of goods that cost $1 in mid b) What will be the value of a dollar in mid-2015 in constant mid-2012 dollars?

8 Answers Question 4: What is the present value of $10,000, 4 years from now, at an APY of 5%? Present Value PV = A (1 + i) n = A (1 + r/m) mt Answer: APY = = 8, Question 5: What is the present value of $15,000, 10 years from now, at an APY of 3%? Answer: APY = = 11,

9 Answers Question 6: Suppose that inflation proceeds at a constant rate of 2% per year from mid through mid a) Find the cost in mid-2015 of a basket of goods that cost $1 in mid Answer: Annual Rate of Inflation The annual rate of inflation, a (= 100a%). Goods that cost $ 1 in the base year will then cost $ (1+a). cost = ( ) 3 = $1.06 b) What will be the value of a dollar in mid-2015 in constant mid-2012 dollars? Answer: value = 1/(1.02) 3 = $0.94

10 This Time The Consumer Price Index Real Growth

11 Motivating Question How is inflation calculated?

12 The Consumer Price index The official measure of inflation is the Consumer Price Index (CPI) which is the determined by the Bureau of Labor Statistics (BLS). CPI for other year 100 = cost of market basket in other year cost of market basket in base period The base period used to calculated the CPI-U is

13 Question Question: If someone bought a house in mid-1990 for 150,000. What would be the equivalent cost in mid-2012 dollars? Answer: The CPI in 1990 was The CPI in 2012 was so cost in 2012 CPI in 2012 = cost in 1990 CPI in 1990 cost in = cost in 2012 = = 263,

14 Question A 1963 Chevy Bel Air, a classic car today, cost $ 2,400 new in mid How much would that be in 2012 dollars?

15 Question A 1963 Chevy Bel Air, a classic car today, cost $ 2,400 new in mid How much would that be in 2012 dollars? Answer: The CPI in 1963 was 30.6 The CPI in 2012 was cost in = cost in 2012 = = 18,

16 Motivating Question How much money will my investment be worth in today s dollars?

17 Real Growth Under Inflation Real rate of Growth The real annual rate of growth of an investment at annual interest rate r with annual inflation rate a is g = r a 1 + a

18 Question Question: In mid 2013 you put a $1000 into a savings account with APY 1 %. Assuming there is a constant inflation rate of 2 % for the next 3 years, how much money will you have in the account in mid 2016 in constant mid-2013 dollars?

19 Question Question: In mid 2013 you put a $1000 into a savings account with APY 1 %. Assuming there is a constant inflation rate of 2 % for the next 3 years, how much money will you have in the account in mid 2016 in constant mid-2013 dollars? Answer: g = = = A = 1000( ) 3 =

20 Question Question: In mid 2013 you put a $1000 into a savings account. Assuming there is a constant inflation rate of 2 % for the next 3 years, what would the APY of the savings account have to be in order to have $1100 dollars in constant mid-2012 dollars in 3 years?

21 Question Question: In mid 2013 you put a $1000 into a savings account. Assuming there is a constant inflation rate of 2 % for the next 3 years, what would the APY of the savings account have to be in order to have $1100 dollars in constant mid-2012 dollars in 3 years? Answer: ( 1100 = r.02 ) r =

22 Next time Chapter 22 Borrowing models Test a week from Friday over chapters 10, 13, 21 and part of 22.