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?
8 answers
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.
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.
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?
No.
. 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
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.
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.
1 answer