A = P[1 + (r/n)]^nt - How do I solve for t?

Question

If:
A = 1,000,000
P = 35,000
n = 4
r = 8.5%

This gives me the equation:
1,000,000 = 35,000[1 + (.085/4)]^4t

I know that I am supposed to do something with logarithms, because that is the reversal of exponents, but I'm not quite sure what. Or what the base would be. Or how to get there in the first place. Anyone want to help?

Answer 1

Step 1: Divide 35000 over
Step 2: log (or ln) both sides, bringing 4t down as a coefficient.
Step 3: Divide 4log(1+0.085/4) over.
Step 4: t is isolated. Calculator evaluate the left hand side.

Hope this helps

Answer 2

Remember that log (a^b) = b log (a). Also remember that log(ab) = log(a) + log(b), and log(a/b) = log(a) - log(b). This is regardless of the base of the log. So using the standard base-10 log and doing some simplifying along the way, we get:

1,000,000 = 35,000[1 + (.085/4)]^4t
log(1,000,000) = log (35,000[1 + (.085/4)]^4t)
log(10^6) = log (35,000) + log([1 + (.085/4)]^4t)
6log(10) = log (35*1000) + (4t)log[1 + (.085/4)]
6 = log (35) + log(1000) + (4t)log[1 + (.085/4)]
6 = log (35) + 3 + (4t)log[1 + (.085/4)]
3 - log(35) = (4t)log[1 + (.085/4)]
t = [3 - log(35)] / 4log[1 + (.085/4)]
t = [3 - log(35)] / 4log(1.2125)

Now use the calculator to evaluate this

Answer 3

1,000,000 = 35,000[1 + (.085/4)]^4t
[1 + (.085/4)]^4t = 1000000/35000 = 1000/35 = 200/7
Apply log:
(4t) * log[1 + (.085/4)] = log (200/7)
4t = [log (200/7)] / {log[1 + (.085/4)]}
t = [log (200/7)] / {log[1 + (.085/4)]} * (1/4)
t = [log (200/7)] / {log(1 + 0.02125)} * (1/4)
t = [log (200/7)] / [log(1.02125)] * (1/4)
t = [log (200/7)] / [log(1.02125)] * (1/4)
t = 39.858 (corrected to 3 dec places)

Answer 4

Let (1+r/n) = X : then

A=PX^nt: take natural log of both sides to get:

Ln (A/P) = nt (Ln X): With a bit of algebra we get

t= (1/n) Ln (A/P)/ Ln X : subsitute P(1+r/n) for X

Plug in your variables to solve for t

TTFN

Answer 5

need to use log.

Log A = Log P + nt log(1+r/n)

Answer 6

log(1000000/35000)=4tlog(1+(.085/4))
So t=log(28.571)/[4log(1.02125)]
t=1.4559/.0365=39.85