You’ve just learned that you inherited $500,000 from a long-lost relative. Now y
ID: 3205170 • Letter: Y
Question
You’ve just learned that you inherited $500,000 from a long-lost relative. Now you need to decide how to invest the money. Your grandfather recommends that you put the money in your local savings and loan, which has an insured savings account earning 3.5% nominal interest rate annually, compounded monthly. Your cousin, who is a stockbroker, recommends that you invest the money in the stock market. She points out that her clients have been earning an average rate of return of 8.0% per year over the last 20 years depending on what stock you choose, although at present the returns are negative.
A) Assuming that you want to use the money for retirement in 40 years, should you listen to your grandfather or your cousin? Give your reason(s).
B) After you retire, you want to be able to earn at least $50,000 per year in 2014 dollars. How much income will you need to earn in 2054 dollars? Assume the inflation rate is 2.0% per year.
C) You retire in 2054 and you want to maintain your income in 2054 dollars the same as you calculate from b). Assume your money will be in the savings account earning a constant 5.0% annually (this is the nominal rate!) and the interest made on the account is the only source of your income. How much money do you need to put in the saving account in 2051? Assume the inflation rate is still 2.0% per year since 2054. Hint: Plot the cash flow diagram for yourself. In this case you take the same amount of money from the account every year and leave the principle (the money you put in the beginning) to be the same to the next year. Also for this problem you need to decide to use the real interest rate or the nominal rate.
Explanation / Answer
A)
Money Inherited = $500,000
Local savings and loan = 3.5% nominal interest rate annually, compounded monthly
stock market = 8.0% per year
A) to compare the two lets check the money available after years
by using compund interest formula
FV = P (1 + r / n)Yn
where P is the starting principal, r is the annual interest rate, Y is the number of years invested, and n is the number of compounding periods per year. FV is the future value, meaning the amount the principal grows to after Y years.
if invested in local savings acont = $2,023,472.54
if invested in stock market = $10,862,260.75
As the amount invested in the stock market will be much higher than the local saving account , the money should be invested in the stock market.
B)
inflation rate = 2%
money required in 2014 = $5000
therefore money required in 2054 is calculated using the formula FV = P (1 + r / n)Yn
= 50000(1+2)40
= $110,401.98
C)
Money needed per annum is $110,401.98
there lets assume x ammount be present in the bank account in 2054.
there 5% of x should be $110,401.98
i.e. 5 * x / 100 = 110401.98
x = $2,208,039.6 in year 2054
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