Thursday

August 21, 2014

August 21, 2014

Posted by **Thara!** on Saturday, April 10, 2010 at 9:03pm.

- Math! plz help! -
**DQR**, Sunday, April 11, 2010 at 3:04pmThe first part seems easy enough, but we're not at all sure about the second part. The investment is earning 7% compounded semi-annually until he turns 18, so that means the original $4,500 will have become ((1.07)^36) x $4,500 = $51,407.74 on his 18th birthday. So far, so good.

Now, we're assuming (and we could easily be wrong about this) that this "4.75% compounded and paying out quarterly" means that the annuity is accumulating interest at this rate annually, BUT paying out 16 equal payments over the four years that he's at college - at the end of which time there will be nothing left. We therefore have to find out what each of those payments will be, bearing in mind that the interest will be accumulating on a different amount every quarter. Tricky....

Suppose the quarterly payment is Q, that the annuity is purchased for A (which we already know is $51,407.74, but A is easier to write), and P is the quarterly interest rate on the annuity (i.e. whatever rate will give us 4.75% per annum). We're also going to assume that he withdraws his quarterly payment at the END of each quarter, so during the first quarter he's earning interest on the full amount. So the amount left at the end of each quarter should be....

A(1+P) - Q

(A(1+P) - Q)(1+P) - Q

((A(1+P) - Q)(1+P) - Q)(1+P) - Q

(((A(1+P) - Q)(1+P) - Q)(1+P) - Q)(1+P) - Q

P is easy enough to find: it is whatever value will give us (1+P)^4 = 1.0475, i.e. P = 1.167%. With that value, the above series of recursive relationships with any given value of Q can be fed into 16 successive cells in a column of Excel easily enough - and we then need to find Q such that the final amount in the 16th cell is zero. Having done just that, we reckon that the quarterly payment to him should be $3,540.91, which would leave him with just one cent in his account at the end of the fourth year. But arriving at that algebraically is beyond us - and obviously you'll need to show your working to get the marks, so the best we can do is show you how the problem might be tackled, and offer a possible answer to check yours against if you can do it. Sorry!

**Related Questions**

math help plz! - When Cody's son was born, he put $4,500 in an investment that ...

Annuity! - When Raisel's son was born, she put $7,500 in an investment that ...

math! - When Raisel's son was born, she put $7,500 in an investment that earns 5...

precalc - A $5000 investment earns 7.2% annual interest, and an $8000 investment...

Math - How to calculate this? 4 year term investment. The investment offers a ...

pre calculus - Which is worth more after 5 years, an investment of $1000 at 5% ...

math - what will investment of 10 000 Yen amount to after 5 years if it earns 8...

math - what will the value of my investment be on $3000 at 6% annual interest ...

Foundations Math 12 - Jie is investing $15000 and is choosing between two ...

Pre-Calculus - How to solve this problem by using logarithm: David inherits $...