after twelve monthly deposits of $400 at 12% compounded monthly, find the amount of an annuity.
please help me:(
DEP. = $400 per mo @ 12% = 1% MPR.=.01
1. BAL = 400* 1.01 = 404.
2. BAL = ( 404 + 400 )*1.01 = 812.04
3. BAL = (812.04 + 400)*1.01=1224.16
4. BAL= (1224.16+400)*1.01=1640.40
5. BAL= (1640.40+400)*1.01=2060.81
6. BAL= (2060.81+400)*1.01=2485.42
7. BAL= (2485.42+400)*1.01=2914.27
8. BAL= (2914.27+400)*1.01=3347.41
9. BAL= (3347.41+400)*1.01=3784.88
10.BAL= (3784.88+400)*1.01=4226.73
11.BAL= (4226.73+400)*1.01=4673.00
12.BAL= (4673.00+400)*1.01=5123.73
Couldn't find a single formula to
do the calculations, so I had to
calculate the BAL. at the end of
each month to get the BAL. at the
end of 12 months.
this,
To find the amount of an annuity after twelve monthly deposits of $400 at a 12% interest rate compounded monthly, you can use the formula for the future value of an ordinary annuity:
Future Value = Payment [(1 + interest rate)^(number of periods) - 1] / interest rate
In this case, the payment is $400, the interest rate is 12% (or 0.12), and the number of periods is 12 (as it is compounded monthly for a year).
Plugging these values into the formula, we get:
Future Value = $400 [(1 + 0.12)^(12) - 1] / 0.12
Now, let's calculate it step by step:
1. First, let's simplify the expression inside the brackets:
(1 + 0.12)^(12) = 1.12^(12) ≈ 3.10585
2. Now, let's substitute this value back into our formula:
Future Value = $400 [3.10585 - 1] / 0.12
3. Subtracting 1:
Future Value = $400 [2.10585] / 0.12
4. Division:
Future Value ≈ $7,019.25
Therefore, the amount of the annuity after twelve monthly deposits of $400 at a 12% interest rate compounded monthly would be approximately $7,019.25.