compound and interest Using the below values please calculate the amount accumulated (future value) *Initial principal=$2000 *Interest Rate=9% *Number of years 7 *Monthly compounding
For monthly compounding (as opposed to annual), we need to calculate two things:
1. the monthly compounding interest:
annual interest/12=9%/12=0.75%=0.0075
2. the number of periods to cover 7 years
= 7*12 =84 (months)
The future value
= Principal * (1+interest)^periods
= 2000*1.0075^84
= $3746.40
(compare to simple interest
2000*(1+0.09*7)= $3260 < $3746, OK)
To calculate the future value (amount accumulated) using compound interest, we need to use the formula:
A = P(1 + r/n)^(nt)
Where:
A = future value (amount accumulated)
P = initial principal (starting amount)
r = interest rate (in decimal form)
n = number of compounding periods per year
t = number of years
In this case, the given values are:
P = $2000
r = 9% (or 0.09 as a decimal)
n = 12 (since it's monthly compounding - 12 months in a year)
t = 7
Substituting these values into the formula, we have:
A = 2000(1 + 0.09/12)^(12*7)
Now, let's calculate the future value:
A = 2000(1 + 0.0075)^(84)
A = 2000(1.0075)^(84)
A ≈ 2000(1.718083859)
A ≈ $3,436.17
Therefore, the amount accumulated (future value) after 7 years of monthly compounding at an interest rate of 9% with an initial principal of $2000 is approximately $3,436.17.