## Finance: $1K dep at 6% semi-annual for 18yrs; find balance Topics that don't fit anywhere else. andy44 Posts: 7 Joined: Sat Mar 21, 2009 12:40 pm ### Finance:$1K dep at 6% semi-annual for 18yrs; find balance

Back when Nathan was born, his mother deposited $1,000 in an account paying 6% compounded semi-annually. He has just turned 18. A) How much money is in the account? B) Suppose, on Nathan's 10th birthday, that his mother had been able to add$1,000 more to the account.what is the account balance at the end of the same 18 years?

stapel_eliz
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Back when Nathan was born, his mother deposited $1,000 in an account paying 6% compounded semi-annually. He has just turned 18. A) How much money is in the account? Use the compound-interest formula you've memorized: . . . . .$A\, =\, P\left(1\, +\, \frac{r}{n}\right)^{nt}$ ...where "A" is the ending amount, "P" is the beginning amount, "r" is the interest rate (as a decimal), "n" is the number of compoundings per cycle, and "t" is the number of cycles (usually "years"). In your case, the set-up would be: . . . . .$A\, =\, 1000\left(1\, +\, \frac{0.06}{2}\right)^{2\times 18}$ Of course, n = 2 because "semi-annually" means "twice a year". Simplify to get your answer. B) Suppose, on Nathan's 10th birthday, that his mother had been able to add$1,000 more to the account.what is the account balance at the end of the same 18 years?
This works just like the previous one, expect that it's in two pieces. You'd find the value at the end of the first ten years:

. . . . .$A_{10}\, =\, 1000\left(1\, +\, \frac{0.06}{2}\right)^{2\times 10}$

Then you'd add another thousand bucks, and use this as your "P" in the second bit, being the last eight years:

. . . . .$A_{18}\, =\, (A_{10}\, +\, 1000)\left(1\, +\, \frac{0.06}{2}\right)^{2\times 8}$

Try to "carry" as much as you can inside your calculator, so as to minimize round-off error.

andy44
Posts: 7
Joined: Sat Mar 21, 2009 12:40 pm

### Re: Finance: \$1K dep at 6% semi-annual for 18yrs; find balance

i get 2898.278328 and 4502.984767 is this teh right ans?

stapel_eliz
Posts: 1628
Joined: Mon Dec 08, 2008 4:22 pm
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You appear to have done the mathematics correctly, but now you need to interpret your numerical values in terms of the original exercise.

1) For which part of the exercise does each numerical value stand? You should make this clear in your answers.

2) How many decimal places are customarily used for "dollars and cents"? You should use only this many in your answers.

3) What symbol indicates "dollars", and what is its proper placement? You should use this symbol, properly placed, in your answers.