Find the amount (future value) of the ordinary annuity. (Round your answer to the nearest cent.)
$950/month for 18 years at 2%/year compounded monthly
A direct application of the formula again.
Show me your steps
To find the future value (amount) of an ordinary annuity, you can use the formula:
Future Value = Payment x ( (1 + interest rate)^(number of periods) - 1 ) / interest rate
In this case, the payment is $950/month, the interest rate is 2% (or 0.02 decimal) per year, compounded monthly, and the number of periods is 18 years (or 216 months).
First, convert the annual interest rate to the monthly interest rate by dividing it by 12: 0.02 / 12 = 0.0016667.
Next, substitute the values into the formula:
Future Value = $950 x ( (1 + 0.0016667)^(216) - 1 ) / 0.0016667
Now, let's calculate this expression step by step:
1. Calculate ( 1 + 0.0016667 )^(216):
( 1 + 0.0016667 )^(216) = 2.0091356
2. Substitute the calculated value back into the formula:
Future Value = $950 x ( 2.0091356 - 1 ) / 0.0016667
3. Calculate (2.0091356 - 1):
(2.0091356 - 1) = 1.0091356
4. Substitute the value back into the formula:
Future Value = $950 x 1.0091356 / 0.0016667
5. Calculate the final result:
Future Value = $572,657.51 (rounded to the nearest cent)
Therefore, the amount (future value) of the ordinary annuity is approximately $572,657.51