Instead of spending the $50 a month you receive, you decided to invest it in your money market account at your bank. Assuming you will earn an average of 5% each year and inflation is forecasted to 2.5% a year, how much have you effectively earned after ten years? (Hint: must use a two formulas to solve this question) In other words, after you have factored out the effects of inflation, how much purchasing power do you have?
Can you please help me with what two equations I'm supposed to use? I was thinking the first one is the Future Value Annuity:
FVA = 50[(1+(.05/12))^(10x12)-1)/(.05/12))]
but I also wondered if it was just Future Value. Can you help me out with what to do after that?
The FVA formula gives you the effective amount at the future date. You may want to convert the amount back to present value, using the inflation rate.
The formula is
PV=FV/(1+i)^n
where
i=inflation rate
n=number of years.
Certainly! To determine the amount of money you have effectively earned after ten years, factoring in the effects of inflation, you can use two formulas: the future value of an annuity and the future value formula.
The first equation you mentioned is the future value annuity (FVA) formula, which calculates the future value of a series of equal payments made over time. However, in this scenario, you are not making equal monthly payments, but rather investing a fixed amount each month. Therefore, this formula is not applicable here.
Instead, you can use the future value (FV) formula, which calculates the future value of a lump sum investment. The formula is:
FV = P(1 + r)^n
Where:
FV = future value
P = principal amount (initial investment)
r = rate of return per compounding period (annual interest rate divided by the number of compounding periods in a year)
n = number of compounding periods (years multiplied by the number of compounding periods in a year)
In this case, the principal amount (P) is $50, the rate of return (r) is 5% divided by 12 (to account for monthly compounding), and the number of compounding periods (n) is 10 years multiplied by 12 months.
Using this formula, you can calculate the future value of your monthly investments after ten years. However, this value doesn't account for the effects of inflation.
To adjust for inflation, you can use the following formula:
Effective Earnings = FV / (1 + inflation rate)^n
Here, the inflation rate is 2.5% per year, and n represents the same number of compounding periods as before (10 years multiplied by 12 months).
By plugging in the values into this formula, you can calculate how much you have effectively earned after ten years, factoring in the effects of inflation. This adjusted value will give you a better understanding of your purchasing power over time.
I hope this explanation helps you solve the problem! Let me know if you have any further questions.