Future Value of Investments after 8 Years
How much will each investment be worth after 8 years?
Option 1 $ _____ Option 2 $ _____
Answer:
After 8 years, investment Option 1 would be worth approximately $9063.70 and Option 2 would be worth approximately $9084.24.
Option 1: To calculate the future value of an investment compounded annually, we can use the formula:
FV = P(1 + r/n)^(nt)
where FV is the future value, P is the principal amount, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years.
Using this formula for Option 1:
FV = $5000(1 + 0.08/1)^(1*8)
FV = $5000(1.08)^8
FV ≈ $9063.70
Option 2: For continuous compounding, we can use the formula:
FV = Pe^(rt)
where e is the base of natural logarithm.
Using this formula for Option 2:
FV = $5000e^(0.07*8)
FV ≈ $9084.24
Therefore, after 8 years, Option 1 would be worth approximately $9063.70 and Option 2 would be worth approximately $9084.24.