Final answer:
The future value of a $100,000 inheritance, invested at a 6% annual interest rate and allowed to grow for 30 years is $574,349.57. Since this exceeds the $500,000 retirement goal, no additional annual savings are required.
Step-by-step explanation:
To calculate the future value of an inheritance of $100,000 received in 10 years and allowed to grow at a 6% annual interest rate for an additional 30 years until retirement, we use the compound interest formula:
FV = P × (1 + r)n
Where:
- FV is the future value of the investment,
- P is the principal amount ($100,000),
- r is the annual interest rate (6% or 0.06), and
- n is the number of years the money is invested (40 - 10 = 30 years).
So: FV = $100,000 × (1 + 0.06)30
FV = $574,349.57 (rounded to two decimal places)
To find out how much you need to save in addition to your inheritance to reach the $500,000 retirement goal, you should account for the future value of the inheritance and calculate the remaining amount that needs to be saved. You then divide this number by the number of saving years to find the annual savings required.
So: Amount to save = Retirement goal - FV of inheritance
Amount to save = $500,000 - $574,349.57
Since the future value of the inheritance already exceeds the retirement goal, no additional savings are required. However, if the retirement goal was higher or interest rate was lower, you would use similar calculations to find the annual savings amount.