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.