leozap1
  • leozap1
A $6,000.00 principal earns 8% interest, compounded semiannually. After 35 years, what is the balance in the account ok so do I add 8% of the balance 35 times? (Once for each year)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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terenzreignz
  • terenzreignz
This is compound interest, and it's compounded semianually, it actually means the effective interest rate is 4% for every semi-annum, or half-year. So, if there are 35 years, how many half-years? :D
leozap1
  • leozap1
70
terenzreignz
  • terenzreignz
That's right :) Now, this is compound interest, so, the balance earns interest every time. What you said, which is, adding 8% of the balance every time, is technically what we do, but that sounds rather tedious. Here's a better way: The balance, or accumulated value, after n-years is given by \[\Large P\left(1+ \frac{r}{m}\right)^{mn}\] Where P is the present value, or principal r is the compounded rate of interest m is the number of divisions per year (in this case 2, since it's compounded semianually, or per half-year) n is the number of years. Just plug in, and you'll have your answer ^_^

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terenzreignz
  • terenzreignz
n is still 35 years okay? And don't forget that r should not be in percent, but in decimal: 8% = 0.08
leozap1
  • leozap1
None of the answers are in that forum though
terenzreignz
  • terenzreignz
P is 6000, so... we basically have \[\Large 6000(1.04)^{70}\]
leozap1
  • leozap1
Were did you get 1.04?
terenzreignz
  • terenzreignz
\[\Large 1+ \frac{r}m\] r = 0.08 since the rate is 8% m is 2, since it's compounded per half-year (semianually) So... \[\Large 1+ \frac{0.08}2= 1+0.04=1.04\]
leozap1
  • leozap1
Oh
leozap1
  • leozap1
Is there a easier way to multiply it out Here are the answers a. 22,800 b. 39,600 c. 88,712 d. 93,429
terenzreignz
  • terenzreignz
No... I'm sure they won't make you do this if you didn't have a calculator at your disposal. And yes, the answer is in the choices...
leozap1
  • leozap1
1.04^70 Do I multiply that out first?
terenzreignz
  • terenzreignz
Sure. It doesn't really matter... but that does seem the most logical way.. (please tell me you have a calculator)
leozap1
  • leozap1
Yes I do
terenzreignz
  • terenzreignz
then... just key in the stuff, and you'll be set ^_^
leozap1
  • leozap1
It will still take for ever
terenzreignz
  • terenzreignz
Oh... not a scientific calculator? LOL no matter, just google 1.04^70
terenzreignz
  • terenzreignz
And then multiply it to the principal, 6000
leozap1
  • leozap1
I dotn have oen of them
terenzreignz
  • terenzreignz
Yeah, google also does calculating.
terenzreignz
  • terenzreignz
Just google 1.04^70
leozap1
  • leozap1
I used online calculator and it say its only 15.571618 that cant be right
terenzreignz
  • terenzreignz
Yes, of course, that's not it yet, you still have to multiply that to the principal, 6000, remember? :P
leozap1
  • leozap1
Oh yah lol
leozap1
  • leozap1
Its D. :)
terenzreignz
  • terenzreignz
That's right ^_^ Good job...
leozap1
  • leozap1
Thanks :)
terenzreignz
  • terenzreignz
Might want to keep this in mind, in case of more questions like this: \[\Large P\left(1+ \frac{r}{m}\right)^{mn}\] But remember, a formula can get you only so far... and not very far if you don't know what it's for ^_^
leozap1
  • leozap1
Can you help me with another one please A boat cost $92,000.00 and the depreciates in value by 15% per year. How much will the boat be worth after 10 years? a. 18,112.45 b. 78,200.00 c. 18,941.98 d. 69,000.00
terenzreignz
  • terenzreignz
ohh... depreciate... it's similar, except the rate is in the negative instead of positive, since the value is decreasing. Still this formula : \[\Large P\left(1+ \frac{r}{m}\right)^{mn}\] But take r = -15% or -0.15 and m = 1 since it's yearly; ie; the year is not divided.
leozap1
  • leozap1
I am still confused
leozap1
  • leozap1
Sorry I just don't understnad
terenzreignz
  • terenzreignz
Evaluate: P = 92000 r = -0.15 m = 1 n = 10 yrs
leozap1
  • leozap1
Ok so then it would be 0.925^10
terenzreignz
  • terenzreignz
m=1, okay? not 2. Because this is per year, not per half-year.
leozap1
  • leozap1
Oh
leozap1
  • leozap1
So 0.85 ^ 10?
terenzreignz
  • terenzreignz
Yes, and when that's done, multiply that to the principal.
leozap1
  • leozap1
= 0.19687440434072?
terenzreignz
  • terenzreignz
and multiply to the original value.
leozap1
  • leozap1
A?

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