James Johnson, a recent graduate of a nationally recognized MPA program wants to be able to travel around the world. James does not have enough money at this time, but believes he can save up enough money to travel around the world in ten years. If he currently has $15,000 to invest and estimates he can earn 10% compounded annually on his investment, how much must James put aside at the end of each of the next ten years in order to accumulate the $100,000 he anticipates will be needed to fulfill his dream?
To determine how much James needs to save each year to accumulate $100,000 in ten years, we can use the concept of future value and the formula for calculating the future value of an investment with compound interest.
The formula for future value (FV) is given by:
FV = PV * (1 + r)^n
Where:
FV = future value
PV = present value (initial investment)
r = interest rate per compounding period
n = number of compounding periods
In this case, the present value (PV) is $15,000, the interest rate (r) is 10% (or 0.10), and the number of compounding periods (n) is 10 years.
Using the formula, we can calculate the future value (FV) that James needs to accumulate:
FV = $15,000 * (1 + 0.10)^10
FV = $15,000 * 1.10^10
FV = $15,000 * 2.5937
FV ≈ $38,906.16
So, James needs to accumulate approximately $38,906.16 in ten years. However, his goal is to accumulate $100,000. Therefore, he needs to save an additional amount each year to reach his target.
To calculate the additional amount James needs to save, we subtract the future value he will have from the target amount:
Additional amount = Target amount - Future value
Additional amount = $100,000 - $38,906.16
Additional amount ≈ $61,093.84
Therefore, James needs to put aside approximately $61,093.84 at the end of each of the next ten years in order to accumulate the $100,000 needed to fulfill his dream of traveling around the world.