given P=$830, r=6%, and A=$2075 years, find t

Question

I don't know how to find t. Also, just for future reference, how would I find the other letters as well? Thanks.

Answer 1

Hi Jenson,

 

I worked this problem under the assumption of simple interest, and I am finding the answer to be a bit odd.  Not that it couldn't be correct - I simply find it very unusual, because it came out to 25.  If that is in years, it does not make sense to me that you would have simple interest over 25 years with no compounding.

 

I need for you to check the accuracy of the numbers presented, and also confirm that it's simple interest.  (I'm also wondering why you wrote "A=$2075 years"?)  If it compounds, we have to know what the compounding period is, even if it's just annual.

 

I can run an example of simple interest, solving for t, using some numbers that make more sense.

The equation is A = P + Prt.  (Prt = interest, so the principle + the interest = maturity value)

 

You can factor out the P, and it becomes:

A = P (1 + rt)

 

This is the form I find works best most often.

 

I'm going to use A = 206, P = 200, r = 6% and solve for time, given it's in months:

 

206 = 200 (1 + .06t)   (Don't forget to move the decimal place to the left two places on the rate.)

 

Remember that we are trying to isolate to the term with the t.  We need to get rid of the 200 first since it's outside the parenthesis, so we divide both sides by 200:

 

206 / 200 = [200 (1 + .06t) ] / 200 -->

 

1.03 = 1 + .06t  (You can remove the parenthesis at this point.)

 

Now we need to get rid of the 1, the other term, so we minus 1 from both sides:

 

1.03 - 1 = 1 + .06t - 1 -->

 

.03 = .06t

 

Then we divide both sides by .06 to get our t:

 

.03 / .06 = .06t / .06    (the .06 just cancels out) -->

 

.5 = t

 

 

The tricky part about time is that we would normally use it in fractional form, but the answer comes out in decimal form.  This is where you need to know the time, whether it's in months or days (or years).

 

This one is in months as I stated, so we would take our answer and multiply by 12 months:

 

.5 (12) = 6 months

 

When we have time given, we would use 6/12 for that.  6/12 = .5 as a decimal.  Multiplying by the 12 just gives us the answer in months without the fraction.  This is an extra step that needs done to solve for time, that you have to remember to do!

 

If it were days you would take your final answer and multiply by 360 (or 365 depending what your book uses).

 

Your book may state that it will always be in months or something, so you need to look for that.

 

The answer I got for your numbers is 25.  That could be 25 years, but that would be rather odd for simple interest.  And multiplying by 12 or 360 just makes it worse.  So I question that answer.  If you think the information is correct, go ahead and try solving it and see if you can get the 25.