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Things You Should Know
Time Value of Money problems
All the readings including WSJ ‘little’ book Stocks: trading, calculating returns Mutual Funds Stock Indexes
TVM How to work your calculator
Setting different compounding periods
PV and FV of single cash flow
PV and FV of multiple cash flows Annuities Annuities due Perpetuities
Translating word problems into TVM
TVM
Finding the single unknown PV, FV, N, I/YR, PMT
Different ways of stating interest rates APR, EAR, Add-on, Points
Combining PV and FV problems Saving for retirement
Comparing different choices using TVM e.g. Lease vs. Buy
Before you begin TVM Read the problem and determine
compounding period
Find out what is asked
Check and set P/YR and BEG/END keys
Clear all memory
Example 1
First Simple Bank pays 6% compounded quarterly whereas First Complex Bank pays 6% compounded continuously. You deposit $15,000 for 3 years in each bank, which account will have more and by how much more?
Answer: $23.98
Example 1 (contd.)
What are the EARs on the two accounts?
Answer: Quarterly: 6.13% Answer: Continuously: 6.18%
Note:
When you have continuous compounding problem, you must use the formula (unless your calculator has continuous compounding function - e.g. 17B)
When you use any formula, enter interest rate in decimals!
Example 2
At 9% interest rate compounded monthly, how many years does it take to quardruple your money?
Answer: 15.46 years
Example 3
You are scheduled to receive $17,000 in two years. When you receive it, you will invest it for six more years at 6 percent per year. How much will you have in eight years?
Answer: $24,114.82
Example 4 Calculate the interest rate charged by a
car dealer when you buy a $14,000 car and are asked to make $349 monthly payments for four years.
Answer: 9.09% per year APR
What is the EAR on the loan? Answer: 9.48% EAR
Example 5
You make 12 monthly payments of $500 starting immediately into an account that earns 8.5% APR compounded monthly. How much will you have at the end of the year?
Answer: $6,283.55
Example 6
Credit card co’ offers 6.9% per year for first 6 months and 22% thereafter, both compounded monthly. You transfer $3,000 balance. How much interest will you owe at the end of the first year?
Answer: $462.59
Example 7 Calculate the interest, principal of your last
payment and balance owed on a 30-year, $325,000 mortgage after you have made monthly payments for 23 years. Interest is 11% APR compounded monthly.
Answers:Interest: $1,670.03Principal: $1,425.02Balance: $180,760.02
Example 8 Your friend is celebrating 35th birthday
and wants to retire at age 65. She wants to withdraw $10,000 on each birthday for 15 years in retirement. A credit union offers 11% per year interest.How much must she deposit every year?
Answer: $361.31
Example 8 continued
If she just inherited money and wants to make one lumpsum deposit today, what amount must she deposit?
Answer: $3,141.17
Example 8 (contd.)
Your friend’s employer will contribute $100 every year. Also, she expects $15,000 from family trust on her 55th birthday which she will put into retirement a/c. What amount must she deposit annually to meet her goals?
Answer: $47.31
Example 9
A check cashing store makes a 1-year ‘discount’ loan of $12,000 by deducting interest at 13% per year immediately. Interest deducted: 12,000 * .13 = $1,560You get: 12,000 - 1,560 = $10,440
What is the EAR on the loan? Answer: 14.94%