suppose you want to invest $60,000 for ten years. You can invest your money in a CD that earns 4% interest, compounded quarterly and has no risk, or you can invest your money in futures that ear 10% interest, compounded quarterly. However, the second investment has a 25% chance of failing and if it does, you lose all of your money.
a.) how much will someone have in 10 years if CD was chosen.
c.) If someoe choses to invest in futures, how much money will you have in 10 years if the investment succeeds? What investment would you choose?
a. P = Po(1+r)^n
Po = $60,000.
r = (4%/4)/100% = 0.01 = Quarterly % rate expressed as a decimal.
n = 4Comp./yr. * 10yrs. = 40 Compounding
periods.
P = ?
c. Same procedure as a.
a.) To calculate the amount you will have in 10 years if you choose the CD option, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal amount (initial investment)
r = the annual interest rate (4% or 0.04 in this case)
n = the number of times interest is compounded per year (quarterly, so 4 times)
t = the number of years
In this scenario, your principal amount is $60,000, annual interest rate is 0.04, interest compounded quarterly, and the time is 10 years.
Plugging these values into the formula, we get:
A = 60000(1 + 0.04/4)^(4*10)
Simplifying the expression within the parentheses:
A = 60000(1 + 0.01)^(40)
A = 60000(1.01)^(40)
Using a calculator or a spreadsheet, you can evaluate the exponential term to find the future value:
A ≈ $97,204.45
So, if you choose the CD option, you will have approximately $97,204.45 after 10 years.
c.) If you choose to invest in futures, there are two scenarios: the investment succeeds or fails.
If the investment succeeds, we can use the same compound interest formula as above, but with an annual interest rate of 10% (or 0.10) since that's the rate of return for the successful investment. Plugging the values into the formula:
A = 60000(1 + 0.10/4)^(4*10)
Simplifying:
A ≈ $172,432.68
Therefore, if the investment succeeds, you will have approximately $172,432.68 after 10 years.
However, there is a 25% chance that the investment fails, in which case you lose all of your money. So, the expected value from the futures investment is:
Expected value = (75% of $172,432.68) + (25% of $0)
Expected value = $129,324.51
To choose which investment option is best, you need to consider your risk tolerance. The CD option guarantees a lower return ($97,204.45) but with no risk of losing any money. The futures option has a potential higher return ($129,324.51) but also the risk of losing everything. It's up to you to decide which option aligns better with your investment goals and risk tolerance.