Derek invests $250 per month for years at 4.8%/a compounded monthly.
How much will his investment be worth at the end of the years?
you can use the annuity formula for future value:
FV=R((1+i)^n-1)/(i)
R=250
i=4.8%/12
n=12*number of years
find the FV
To calculate the worth of Derek's investment at the end of the years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the final amount (the worth of the investment)
P is the principal amount (the initial investment)
r is the annual interest rate (expressed as a decimal)
n is the number of times the interest is compounded per year
t is the number of years
Given:
P = $250 per month
r = 4.8% (expressed as a decimal, so 0.048)
n = 12 (monthly compounding)
t = number of years
To calculate the total amount Derek will have at the end of the years, we need to sum up the compound interest for each monthly investment over the specified period.
First, we need to calculate the total number of monthly investments made by multiplying the number of years by 12:
Number of investments = number of years × 12
Next, we can substitute the values into the formula and calculate the final amount:
A = $250 × (1 + 0.048/12)^(Number of investments)
Keep in mind that Derek makes a new investment of $250 every month for the specified number of years.
Using this formula, we can calculate the worth of Derek's investment at the end of the years.
at the end of how many years ????
amount = 250 (1.004^(number of months) - 1)/.004