Final answer:
The question involves finding the annual payment Charlie Munger must make to save up $14,046 at the end of 10 years with a 9% annual interest. This is accomplished using the future value annuity formula, rearranging it to solve for the annual payment based on the given interest rate and time period.
Step-by-step explanation:
The student is asking about the calculations involved in determining the amount that needs to be saved annually in order to accumulate a certain sum of money, given a specific interest rate and compounding period. This type of calculation is rooted in the mathematical concept of the future value of an annuity, which is used in personal finance planning. In Charlie Munger's case, he wishes to have $14,046 at the end of 10 years at an annual interest rate of 9%. To solve this, we use the future value annuity formula:
FV = P × [((1 + r)^n - 1) / r]
Where:
- FV is the future value of the annuity
- P is the annual payment (what we are solving for)
- r is the annual interest rate (9% or 0.09)
- n is the number of periods (10 years)
Since we are solving for P, we must rearrange the formula and plug in the known values:
P = FV / [((1 + r)^n - 1) / r]
After substituting the numbers into the formula, we can calculate the amount Charlie needs to save annually to reach his target of $14,046 by the end of 10 years with a 9% annual return.