Final answer:
Donald can invest his $5,000 in a fund with a yearly return of 7% for 18 years using the compound interest formula to grow this to a future value of $16,931.85, which will be available for his daughter's education on her 18th birthday.
Step-by-step explanation:
Donald wants to finance his daughter's future study by investing his $5,000 lottery winnings into a fund with a 7% yearly return for 18 years. To calculate the future value of the investment, we can use the compound interest formula:
FV = P(1 + r/n)^(nt)
Where:
- FV is the future value of the investment,
- P is the principal amount ($5,000),
- r is the annual interest rate (0.07),
- n is the number of times that interest is compounded per year (assumed to be 1 in this case), and
- t is the number of years the money is invested (18 years).
When we plug the values into the formula, we get:
FV = $5,000(1 + 0.07/1)^(1*18)
Therefore:
FV = $5,000(1.07)^18
Now we calculate:
FV = $5,000(3.38637)
FV = $16,931.85
So, the amount available on the 18th birthday of Donald's daughter would be $16,931.85, when rounded to the nearest cent.