Session 16

Tax- advantage investing for retirement

401K plans: named for paragraph 401k of the internal revenue code - retirement plans you set up for yourself - you put money in a retirement account and it is not taxed when you invest (grows free of taxation) - gets taxed when it comes out based on your tax bracket which will probably be lower Traditional IRA: individual retirement account - not taxed when you invest - grows free from taxation - all withdrawals are taxed at the appropriate tax bracket Roth IRA - taxed when your money is invested - grows free of of taxation - do not have to pay tax on withdrawals

If you invest $130 today and, in 5 years, you have $200 - what was your annually compounded interest? Ignore taxes. A) 9.0% B) 20% C) 53.85% D) 70%

A

If you invest $640 at rate of 13% compounded annually and your tax rate is 35%, what is your after-tax interest earned? A) $54.08 B) $83.2 C) $130.8 D) $224

A

Jim wants to buy a $500,000 house, he already has $10,000 saved. Assuming a 10% annual return and a 30% tax rate, how much will Jim need to save per year to have a 20% down payment in 3 years? A) $27,295 B) $26,190 C) $38,803 D) $40,211 E) $150,136

A

Megan makes a payment of $44,000 a year on her boat. At the end of 20 years, she's paid off her initial $350,000 loan. What was her approximate annual interest rate? A) 11.0% B) 7.9% C) 39.8% D) 2.0% E) 5.4%

A

Suppose you win $1,500, approximately how long it will take for your winnings to reach $4,000 in value if your annual investment returns are 10% (tax-free)? A) 10 years B) 72 years C) 7 years D) 5 years E) 15 years

A

True or False: a 10% investment compounded annually has a lower effective annual rate than a 10% investment compounded quarterly. Ignore taxes. A) True B) False

A

You invest $150 today and in 5 years you will have $300. Ignoring taxes, what is the annual return on your investment? A) 14.9% B) 37.5% C) 50% D) 100%

A

our uncle needs $2,300,000 upon retirement in 30 years to live comfortably. He can invest $18,500 a year to his retirement. What interest rate would his investment need to appreciate at in order for him to meet his goals? A) 8.5% B) 13.8% C) 11.7% D) 4.1% E) 16.3%

A

After tax rate formula

After tax rate= before tax rate* (1-tax rate)

Simple Interest Formula

Annual Interest= Beginning balance * interest rate FV= Principle +(annual interest *number of years)

The rule of 72

Associated with single payments how long it takes to double your money 72/interest rate = number of years 72/number of years = interest rate Lower the interest rate, longer it takes to double your money Only works with single payments

6 years ago, you invested $27,500. The investment has grown to $37,600. What is your average rate of return? A) 3.8% B) 5.4% C) 1.4% D) 2.9% E) 4.6%

B

Dan puts $100 into a savings account that earns 5% (tax-free) interest. In 5 years, he has $105 in the account. Dan earned compounded interest on his principal investment. A) True B) False

B

If Joe wants to pay cash for a $30,000 car in 3 years, how much does he need to save each year if he can earn a 5% tax-free rate of return? A) $8,536 B) $9,516 C) $7,209 D) $5,620 E) $8,933

B

If you invest $3,000 in a start-up and 5 years later your investment is worth $30,000, what was the annual rate of return on this investment? A) 1,000% B) 58.5% C) 200.0% D) 64.6% E) 82.3%

B

In an investment, the after-tax return is the product of the interest rate and the tax rate. A) True B) False

B

In an investment, which of the following is taxed? A) The principal investment B) Interest earned C) The future value D) Investments are tax-exempt

B

On January 1 of this year, you invested $350 at a rate of 5% compounded annually. If your tax rate is 30%, what will the tax on your investment be at the end of the year? A) $5 B) $5.25 C) $17.5 D) $105 E) $175

B

True or False: If Samantha can earn a 5% tax-free interest rate or pay a 30% tax rate on an 8% return, she should invest in the tax free option because it provides a higher tax-adjusted return. A) True B) False

B

True or False: More frequent compounding is bad for investors because it leads to higher costs and lowers their overall return. A) True B) False

B

You have 24 months left until you graduate and you plan on buying yourself a new $20,000 car on graduation day. If you invest $300 a month for the next 24 months earning 4% a month - will you have enough money? A) Yes B) No

B

Jack puts $100 into a savings account that earns 5% (tax-free) interest compounded annually. The amount that Jack will have in the account in 5 years is known as A) Present Value B) Compounded Value C) Future Value D) Total Value

C

Suppose when you turn 25, you begin depositing $3500 every year into a retirement fund that earns 13% (tax-free) interest compounded annually. How much money will you have in your fund when you turn 65? (Round to the nearest thousand) A) $350,000 B) $1,547,000 C) $3,548,000 D) $5,348,000

C

Compounding and future value

Compounding: going from a known value today to an expected but known value in the future. Compounding- means multiply oner a number of time periods, y a number greater that 1.0 Future value: amount of money an investment will grow to by earning a certain rate of return over time Used for: - estimating your portfolio's future value at the time of your retirement - saving fund necessary to finance your child's education - estimating a corporation's yearly budget to fund pension payment requirements

At the beginning of the year, you invested $300 at a rate of 10% compounded annually. At the end of the year, you will have to pay a $12 tax on your investment. What is your tax rate? A) 4% B) 12% C) 30% D) 40%

D

Randy plans to save $10,000 per month for retirement starting today. If he earns a 10% annual return (tax free), compounded monthly, how much will it be worth in ten years? A) $61,445.67 B) $159,374.25 C) $756,711.63 D) $2,048,449.79 E) $9,270,806,881.78

D

The current return on a 10-year U.S. Treasury note is 2%. If you were to invest today and assuming that rate stays fixed indefinitely, how long would it take you to double your investment? Ignore taxes. A) 2 years B) 5 years C) 22 years D) 36 years E) 50 years

D

What is the future value of kicking a smoking habit twenty years from now? Assume $5 a pack per day and an interest rate of 10%. A) $287 B) $36,500 C) $40,150 D) $104,527 E) $254,600

D

You buy a stock at $60 / share expect to earn a 14% return for the next 2 years, what do you expect the stock price will be in two years? A) $98.80 B) $72.38 C) $68.40 D) $77.98 E) $128.40

D

If you invest $15,000 today at a rate of 8.75% (tax-free), how much will it be worth 40 years from now? A) $118,613 B) $317,556 C) $551,724 D) $652,500 E) $429,796

E

If you invest $5,100 a year, what would be the value of this investment at the end of 4 years at an interest rate of 7.75% and a tax rate of 17%? A) $16,986 B) $14,099 C) $19,004 D) $18,968 E) $22,454

E

Travis took out a $225,000 home mortgage with 3.4% interest rate and equal annual payments. How much will he have to pay annually to repay the loan in 15 years? A) $9,084 B) $7,650 C) $5,995 D) $15,000 E) $19,397

E

What payment would you need to make yearly into your savings account if you wanted $250,000 in 6 years, with a tax-rate of 20% and an average market return of 8.5%? A) $6,944 B) $33,652 C) $41,667 D) $57,133 E) $35,126

E

You invest a certain amount of money at 7% interest compounded annually. If in 8 years you have $103.09, what was your principal investment? A) $30 B) $30 C) $40 D) $50 E) $60

E

Future value for multiple payments with compound interest formula

FV= payment *FVMP Factor

Compound Interest Formula

FV=PV*(1+r)^n

The effect of Taxes

Interest rate is usually taxable If it is not, you have to find the after tax rate There will be a tax rate is interest rate is not taxable

Present value formula

PV= FV* (1/(1+r))^n

Present value for multiple payments with compound interest formula

PV= PMT*PVMP Factor

The compounding period: How it affects the future value

Shortening the compounding period increases the effective annual rate More frequent compounding is good for investors- higher effective annual rate higher effective annual rate is more expensive for borrowers annually- one time a year semi-annually- two times a year quarterly- 4 times a year monthly- 12 times a year weekly- 52 times a year

Types of Interest Payments

Simple Interest: Interest to be paid on the original principle invested. The interest is not reinvested. No interest is earned on interest Compound interest: Accumulating interest on an investment for more that one period and reinvesting the interest. Interest is earned on interest - better deal for an investor - we are usually going to use compound interest

You quit your pack a day habit and invest your savings in a stock mutual fund. How much will you have at age 65? Assume your current age is 20 and the cost per pack is $3. Your estimated rate of return would be 12%

cost per pack is $3 - 3*365 days= $1095 per year - PMT=1095 -n=45 -I=12% -PV=0 FV=$1,487,262

Five Financial Function Keys on Calculator

n= number of periods i/y= interest rate or yield PV= present value (today) PMT=periodic payment FV= future value there always has to be one inflow and one outflow Need to have 4 of the numbers in order to find the 5th input