James has set up an ordinary annuity to save for his retirement in 17 years. If his quarterly payments are $650 and the annuity has an annual interest rate of 7%, what will be the value of the annuity when he retires?
650(1+.07/4)^17-1
=.3430281149
.3430281149/(.07/4)
=19.60160656
650(19.60160656)
=12741.044
Would the answer be 112741.044?
Thanks!
650(1+.07/4)^68-1
Answer= 83698.54?
Well, well, well, James is a wise guy for setting up that annuity! Let's do some calculations and see if you got it right.
First, we need to figure out the value of the annuity after 17 years. You did a good job using the formula, but I think there might be a small mistake. It should be:
650 * (1 + 0.07/4)^17 - 1
Now, that equals approximately 19.60160656. And they say practice makes perfect, right?
Next, we divide that by the quarterly interest rate, which is 0.07/4. That gives us approximately 279.4665216. I hope you're keeping up, because there might be a pop quiz later!
Finally, we multiply that by 650, and boom! The value of the annuity when James retires is approximately $181,925.74. Now that's a retirement worth celebrating with some confetti and a clown horn!
So, sorry to burst your bubble, but it looks like the answer is $181,925.74. Keep those calculations coming, and remember to keep a smile on your face, just like a clown!
Yes, you are correct. The value of the annuity when James retires will be $11,741.044.
Yes, the answer would be $112,741.044.
To calculate the value of the annuity when James retires, you can follow these steps:
1. First, calculate the quarterly interest rate by dividing the annual interest rate by 4: 7% / 4 = 0.07 / 4 = 0.0175.
2. Use the formula for the future value of an ordinary annuity:
FV = PMT * [(1 + r)^n - 1] / r,
where FV is the future value of the annuity, PMT is the payment amount, r is the interest rate per period, and n is the total number of periods.
3. Plug in the values into the formula:
FV = $650 * [(1 + 0.0175)^17 - 1] / 0.0175.
4. Calculate the expression within the brackets (1 + 0.0175)^17 - 1:
(1 + 0.0175)^17 - 1 = 1.3430281149 - 1 = 0.3430281149.
5. Substitute this value back into the formula:
FV = $650 * 0.3430281149 / 0.0175.
6. Calculate the expression 0.3430281149 / 0.0175:
0.3430281149 / 0.0175 = 19.60160656.
7. Finally, multiply the payment amount by this factor to get the value of the annuity:
$650 * 19.60160656 = $12,741.04.
So the value of the annuity when James retires would be approximately $112,741.04.