Please help solve this exponential equation. I used A=P(1+r/n)^nt

80,000=20,000(1+0.06/12)^12(23)

Question

Please help solve this exponential equation. I used A=P(1+r/n)^nt

80,000=20,000(1+0.06/12)^12(23)

anonymous · Answer

I really want to see the steps..as this is just a sample problem for me to look at

campbell_st · Answer

well there are no unknowns in this question... its just a case of evaluating. 

it can be simply typed into a calculator as its written...

campbell_st · Answer

the only thing you really need to do is calculate the power... which is 12 x 23 = 276

so enter  20000(1 + 0.06/12)^276

anonymous · Answer

ok one second

anonymous · Answer

that doesnt seem right though...

anonymous · Answer

here is the orignal sample problem

Using the same interest, plus the number of years calculated from problem 1, how much principal would the couple need to invest fund the entire cost of college ($80,000)? 

from the function above we know the interest is 6% and the years is 23.

anonymous · Answer

solving the equation i get like 80,000

anonymous · Answer

i am working on log...im assuming i take the log of both sides somewhere...

campbell_st · Answer

ok..so A the future value is 80000
          P = inknown
          r = 6% p.a. compounded monthly
          t = 23 years... is that the information..?

anonymous · Answer

P is 20,000.  Thats what the couple invested in the first problem.

anonymous · Answer

so from this im assuming the equation is set up as so..80,000=20,
000(1+0.06/12)^12(36)

campbell_st · Answer

so the equation is 

$$80000 = P(1 + 0.06/12 )^{12\times23}$$

then by making P the subject 

$$P = \frac{80000}{(1 + 0.06/100)^{276}}$$

campbell_st · Answer

I think the question is asking how much to invest P to have 80000 

I think Question 1 would have been what is the future value of the when $20000 is invested at...etc

anonymous · Answer

here is problem 1...

	A married couple plan to send their only child to college. They calculate that the first year of college will cost $20,000. If the couple invests $5000 at 6% interest, in how many years will they have at least $20,000 saved? 

this i solved fine and got 23 years...

campbell_st · Answer

quick question... does it say anything about interest compounded monthly or yearly..?

anonymous · Answer

nothing at all

campbell_st · Answer

ok so assume annually... 

so then the equation is 

$$20000 = 5000(1 + 0.06)^n$$

divide both sides by 5000

$$4 = (1.06)^n $$

using logs  base 10

$$\log 4 = n \times \log(1.06)$$

divide both sides by log(1.06)

n = 23.79 years

campbell_st · Answer

say 24 years...

anonymous · Answer

ok so while you were doing this....i came up with this for my answer on #2....$20,202.02

campbell_st · Answer

then to find the principal to cover $80000 in costs its as its shown above...but I'd assume the interest is calculated annually 

$$80000 = P(1 + 0.06)^{23.8}$$

make P the subject

$$P = \frac{80000}{(1.06)^{23.8}}$$

which means you need to invest $20915.78...

campbell_st · Answer

so the amount to invest is between 20000 and 21000 but it depends on the compounding period... if its monthly you will need a slightly smaller amount..

campbell_st · Answer

I have to go... I hope I've helped and not confused... 

good luck

anonymous · Answer

Ok i will ask my teacher tomorrow and see what he says....I really hate these log's though!  and yes you did help!