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?
See question answered:
http://www.jiskha.com/display.cgi?id=1496542812
Yes, you're on the right track with using the Future Value Annuity formula to calculate the future value of your investment. The formula you mentioned is correct:
FVA = P[((1+r)^n)-1]/r
Where:
FVA = Future Value of the annuity/investment
P = Monthly investment amount ($50 in this case)
r = Monthly interest rate (annual rate divided by 12)
n = Number of years (10 years in this case)
Using the given information, the monthly interest rate (r) is calculated as:
r = 0.05/12
Now, you can plug in the values into the formula:
FVA = 50[((1+(0.05/12))^(10*12)-1)/(0.05/12))]
Simplifying this equation will give you the future value of your investment after ten years.
However, to determine the purchasing power after accounting for inflation, you need to adjust for the effects of inflation. The other formula you can use is the Compound Interest formula:
CI = P(1+r)^n
Where:
CI = Compound Interest
P = Principal amount (initial investment)
r = Interest rate (annual rate)
n = Number of years
In this case, the monthly interest rate (r) would be calculated as:
r = 0.025/12
Then, you can calculate the compound interest (CI) using:
CI = 50(1+0.025/12)^(10*12)
This will give you the amount that your initial investment has grown to after ten years, considering the effects of inflation.
To determine the effective purchasing power, subtract the Compound Interest (CI) from the Future Value Annuity (FVA) you calculated earlier. The result will be the amount you effectively earned after accounting for inflation.
Effective Purchasing Power = FVA - CI
I hope this helps! Let me know if you need further assistance.
Sure! To calculate your effective earnings after ten years, you can use two formulas: the Future Value (FV) formula and the Purchasing Power formula.
1. Future Value (FV) Formula:
The first step is to calculate the future value of your monthly investment, assuming an average annual return of 5%. This can be done using the Future Value of an Ordinary Annuity formula:
FV = P * [(1 + r/n)^(n*t) - 1] / (r/n),
Where:
FV = Future Value of the investment
P = Amount of the regular payment ($50)
r = Annual interest rate (5% or 0.05)
n = Number of compounding periods per year (12)
t = Number of years (10)
Plugging in the values, we get:
FV = 50 * [(1 + 0.05/12)^(12*10) - 1] / (0.05/12)
FV ≈ 50 * [1.051161897 - 1] / 0.004166667
FV ≈ 50 * (0.051161897 / 0.004166667)
FV ≈ 50 * 12.27970947
FV ≈ $613.99 (rounded to the nearest cent)
So, after ten years, your investment would grow to approximately $613.99.
2. Purchasing Power Formula:
To account for inflation and determine your purchasing power, you need to use the Purchasing Power formula:
Purchasing Power = FV / (1 + inflation rate),
Where:
FV = Future Value (calculated earlier)
Inflation rate = Annual rate of inflation (2.5% or 0.025)
Plugging in the values, we get:
Purchasing Power = 613.99 / (1 + 0.025)
Purchasing Power ≈ 613.99 / 1.025
Purchasing Power ≈ $599.49 (rounded to the nearest cent)
Therefore, after accounting for inflation, you would effectively have approximately $599.49 in purchasing power after ten years.
Remember that these calculations are approximate and do not take into account any additional factors or fees associated with your money market account.