Question

Albert Einstein reportedly said, “Compound interest is the eighth wonder of the world. He who understands it, earns it. He who doesn’t, pays it.” Regardless of whether Einstein uttered these exact words, the essence of his statement is still immensely powerful and cannot be disputed. For anyone who wants to build lasting wealth, understanding and harnessing the power of compound interest is essential. For the more visual of you, imagine, if you will, building the bottom part of a snowman. It starts with a snowball (or initial investment). You roll it around in the snow and it slowly gets bigger (interest on the investment). A slow and monotonous process until something wonderful becomes apparent – the snowball not only gets bigger and bigger, but at a faster and faster rate (interest on the interest).

Your friend, Mike Szyslak wants be a millionaire, and he found several ways applicable. But he is still hesitating among the various options and comes to you for financial advice. Complete each of the options, below, with your group.

Option 1: He is considering to buy Mega Millions lottery. If the current tax rate on earnings of lottery is 40%, how much money will he have to win on a lottery to become a millionaire?

Option 2: His uncle promised to invest his business $100,000 a year over the next 15 years, and the interest rates over next 15 years are expected be at 5% per annual. Can you help him to know whether the present value of such series of investments make him equivalent to be a millionaire today?

Option 3: He considers to save money and become a millionaire. Starting at age 22, every night Mike takes $5 out of your pocket and put it in a manila envelope. At the end of the year, you place the money from the envelope in a stock fund with an average interest rate of 10%. Will the amount he has in the account ensure him a millionaire when you retire at age 65? What if he starts saving at age 40?

Option 4: He sets aside $50,000 into a saving account now, and will deposit $50,000 into the account at the beginning of each year for next 10 years. If the market rate is 10%, Will he become a millionaire in 10 years?

Option 5: Mike considers to buy 1,000 bonds. The bond is semi-annual coupon bond with 10-year maturity, $1,000 par value bond with a 10 percent annual coupon, and 10 percent annual required rate of return? How much does it cost now if he wants to receive all the coupon payments and par values during the 10-year period? What would be the value of the bond if, just after it had been issued, the expected inflation rate rose by 3 percentage points, causing Mike to require a 13 percent return? What would happen to the bonds' value if inflation fell, and required rate of return declined to 7 percent?

Which of the options would you recommend that Mike choose? Why?

Answer 1

Option - 1:

amount he should win = 1,000,000 / (1 - tax rate)

= 1,000,000 / (1 - 0.4)

= 1,666,666.67 (rounded to two decimals)

Option - 2:

Present value of annuity = P*[1 - (1+r)^-n / r ]

where P = annual investments

r = rate of interest

n = number of periods

present value = 100,000*[1 - (1+5%)^-15 / 5% ]

= $1,037,965.80

Yes it makes him millionaire

Option - 3:

amount per year = 365*5 = 1825

(it is assumed that 365 days per year over the entire 43 years)

future value of annuity =P* [(1+r)^n - 1 / r ]

here n = 65 - 22 = 43

future value = 1825*[(1+10%)^43 - 1 / 10% ]

= $1,081,131

Yes it makes him a millionaire if he start investing at 22

if he start saving at 40

n = 65 - 40 = 25

future value = 1825*[(1+10%)^25 - 1 / 10% ]

= $179,483.4

he will not be a millionaire if he starts investing at 40

Option - 4:

future value of annuity due = P*[(1+r)^n - 1 / r ] *(1+r)

= 50,000*[(1+10%)^10 - 1 / 10% ]*(1+10%)

= $876,558.40

no he will not be a millionaire

Option - 5

when YTM(required rate) = coupon rate bond will trade at par

so when interest rate = 10%

cost of one bond = 1000

total cost = 1000*1000 = 1,000,000

when required return = 13%

value of the bond:

value of 1000 bonds = 1000*834.72 = $834,720

when required return drops to 7%

Value of one bond :

value of 1000 bonds = 1000*1213.19 = $1,213,186.05

Option - 5 when required rate becomes 7% will be better choice as it gives higher wealth.