Using the following values, calculate the amount accumulated (future value):
Initial Principal = $9000
Interest Rate = 8%
Number of years = 9
Monthly Compounding
The formula for compound interest is:
Final amount or future value,
A = PR^n
where
P = principal
R = rate of interest per period, for example, 8% p.a. is 2/3% per month.
R is expressed as 1+rate, so for monthly compounding, R for 8% is 1+8/1200=1.00666667
n = number of periods, month in this case.
This is what i came up with..Dont know if im right.please let me know.
FV= 9000 (1+0.08)9
= 1.08^9 = 1.9990
= 8000 (1.9990) = 17991.00
Future Value = $17, 991.00
What you've done is correct if it is compounded annually.
The question specifies compounded monthly.
What you need to do is to divide the interest into monthly interest rate, namely
R=1+0.08/12
and compound it over n=9*12=108 periods.
It will increase the final amount by about $450.
Got it..Thank you!
You're welcome!
To calculate the future value or amount accumulated, considering monthly compounding, you can use the following formula:
Future Value = Initial Principal * (1 + (Interest Rate / Number of Compounding Periods)) ^ (Number of Compounding Periods * Number of Years)
In this case, the initial principal is $9000, the interest rate is 8%, the number of years is 9, and the compounding period is monthly.
First, we need to convert the annual interest rate to a monthly interest rate. Since there are 12 months in a year, we divide the annual interest rate by 12:
Monthly Interest Rate = 8% / 12 = 0.08 / 12 = 0.0067
Next, we calculate the number of compounding periods by multiplying the number of years by 12 (months):
Number of Compounding Periods = Number of Years * 12 = 9 * 12 = 108
Now we have all the values we need to calculate the future value:
Future Value = $9000 * (1 + 0.0067)^(108)
Using a calculator, the result is approximately $15,823.66.
Therefore, the amount accumulated or future value after 9 years with an initial principal of $9000, an interest rate of 8%, and monthly compounding is approximately $15,823.66.