What will $7,246 deposited monthly accumulate to in 5 years earning 2.50% compounded monthly?
60 months at 0.025/12
7246 * (1 + .025/12)^60
monthly deposits ... need to adjust the formula, as an annuity
Whoops, I did not notice that it was what I call a sinking fund. See:
http://www.math.utep.edu/Faculty/cmmundy/Math%201320/Worksheets/Sinking%20Funds%20&%20Annuities.pdf
here i = 0.025/12
You want FV
Your PMT is 7246
n = 60
i = .025/12
To calculate the accumulation of monthly deposits over a period, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = Accumulated amount after the specified period
P = Monthly deposit amount
r = Annual interest rate (as a decimal)
n = Compounding period per year
t = Number of years
In this case, the monthly deposit is $7,246, the annual interest rate is 2.50%, and it compounds monthly. We need to calculate the accumulation over 5 years.
First, let's convert the annual interest rate to a decimal:
r = 2.50% = 0.025
Next, substitute the given values into the compound interest formula:
A = 7246(1 + 0.025/12)^(12*5)
Now, let's calculate the accumulated amount:
Step 1: Divide the annual interest rate by the number of compounding periods in a year:
0.025/12 = 0.002083333
Step 2: Multiply the number of compounding periods per year by the number of years:
12 * 5 = 60
Step 3: Add 1 to the result from step 1:
1 + 0.002083333 = 1.002083333
Step 4: Raise the result from step 3 to the power of the result from step 2:
(1.002083333)^(60) ≈ 1.13566
Step 5: Multiply the monthly deposit amount by the result from step 4:
7246 * 1.13566 ≈ $8,248.80
Therefore, the accumulated amount after 5 years, with a monthly deposit of $7,246 and an interest rate of 2.50% compounded monthly, will be approximately $8,248.80.