James has set up an ordinary annuity to save for his retirement in 19 years. If his monthly payments are $250 and the annuity has an annual interest rate of 7.5%, what will be the value of the annuity when he retires?
Would the answer be 171.11?
No. How can the value of the annuity be less than the monthly payment?
How would I solve the problem the right way then?
I don't understand how to solve it.
Would the answer be 30336.9?
No.
19 * 12 * 250 = $57,000
That's the amount he's invested. Now multiply that by 1.075 (interest rate) to find the amount of the annuity.
So, would the answer be 4275?
. James has set up an annuity to save for his
retirement in 18 years. His monthly
payments are $250, and the annuity has an
annual interest rate of 8.5% compounded
monthly. When he retires, what will be the
future value of the annuity?
A. $126,823.65
B. $4,781.45
C. $1,148.33
D. $58,327.72
We can begin by calculating the number of monthly payments he will make over the 18 years:
18 years x 12 months/year = 216 monthly payments
Next, we can use the formula for the future value of an annuity:
FV = Pmt x (((1 + r/n)^(n x t)) -1) / (r/n)
Where:
FV = future value
Pmt = monthly payment
r = annual interest rate
n = number of compounding periods per year
t = number of years
Plugging in the given values, we get:
FV = $250 x (((1 + 0.085/12)^(12 x 18/12)) - 1) / (0.085/12)
FV = $250 x (1.085^(12)) x (1 - 1/1.085^(12))/0.085
FV = $250 x 5.4107 x 72.9547
FV = $126,823.65
Therefore, the future value of the annuity when James retires will be $126,823.65, option A.
To calculate the value of the annuity when James retires, we can use the formula for the future value of an ordinary annuity:
\[ FV = P \times \left( \frac{(1 + r)^n - 1}{r} \right) \]
Where:
FV - Future Value
P - Monthly payment amount
r - Monthly interest rate (annual interest rate divided by 12 months)
n - Number of payments (number of years multiplied by 12 months)
Let's calculate step by step.
First, we need to convert the annual interest rate to a monthly rate. Since the annual interest rate is 7.5%, the monthly interest rate would be 7.5% / 12 = 0.075 / 12 = 0.00625.
Next, we need to determine the number of payments. James is saving for retirement in 19 years, so there will be a total of 19 years x 12 months = 228 monthly payments.
Now we can substitute these values into the formula:
FV = $250 × [(1 + 0.00625)^228 - 1] / 0.00625
Calculating this equation, we get:
FV = $250 × (1.00625^228 - 1) / 0.00625
= $250 × (4.648383 - 1) / 0.00625
= $250 × 3.648383 / 0.00625
= $912.09575 / 0.00625
= $145,935.32
So, the value of James' annuity when he retires will be approximately $145,935.32, not $171.11.