your dream car cost $100000 in four years time to purchase. you won a lottery of $65000. can your lottery sum buy you the car should you invest in 90 day 11% treasury bill?
P = Po(1+r)^n.
r = 0.11/yr. * 0.25yr. = 0.0275/qtr.
n = 4 comp./yr. * 4yrs = 16 Compounding
periods.
P = 65000(1.0275)^16 = $100,328.11 in
4 yrs.
90 days = approx. 1/4 of a yr.
To determine if your lottery sum can buy the car in four years, we need to consider the effect of investing in a 90-day 11% treasury bill.
First, let's calculate the future value of your lottery sum after four years, assuming you invest it in the treasury bill.
The formula to calculate the future value (FV) of an investment is:
FV = P * (1 + r)^n
Where:
P = Principal amount (initial investment)
r = Annual interest rate (divide the annual interest rate by the number of compounding periods in a year, in this case, 90 days equals 0.25 years)
n = Number of compounding periods (in this case, 4 years equals 16 quarters)
Using the formula, let's calculate the future value of your lottery sum:
FV = $65,000 * (1 + (0.11/4))^16
FV = $65,000 * (1.0275)^16
FV ≈ $91,226.34 (rounded to the nearest dollar)
After four years, your lottery sum, if invested in the 90-day 11% treasury bill, will grow to approximately $91,226.34.
Now, let's compare the future value of your lottery sum with the cost of your dream car after four years.
Since your dream car will cost $100,000 in four years, and your lottery sum will be approximately $91,226.34, the answer is no. Your lottery sum will not be enough to purchase the car.
Therefore, investing in the 90-day 11% treasury bill will not provide sufficient funds to buy the car after four years.