# A=P(1+r/n)^nt?

Question:A=P(1+r/n)^nt

A=20,000; P=12,500; R=5.75% (which will convert to .0575); n=4; t=unknown. Can you help me find t?

After entering the info, I got: 12,500=20,000(1+(.0575/4))^4t.

I tried working the problem several times. I've gotten a few different answers, but it never matches the answer in the back of the book. Could you work this problem and show me how to get 8.2 as t. I would really appreciate the help. Thank you! =)

I can't figure out how to solve the problem, but the equation should be 20,000 = 12500(1+(.0575/4)^4t because 12500=P not A. Try it again and see if you get the right answer.

Good luck.
I didn't use that formula.
I used B=Pe^rt
B= balance
P= principal
r= rate as a decimal
t= time in years.

It would be
12,500e ^ 0.575t = 20,000
e ^ .0575t = 20,000 / 12,500
.0575t = ln (20,000 / 12,500)
t = ln (20,000 / 12,500) / (.0575)
t = 8.17

The original formula you used was for compound interest. But, that's for n compoundings per year. In this problem, you need to use the continuous compounding formula.

The equation states that A=P(1+(r/n))^(nt) (where we know everything except t). Let's solve it:

A/P=(1+(r/n))^(nt)

A/P=((1+(r/n))^n)^t (this is the tricky point where we need to use logs)

log_10(A/P) = t*(log_10(1+(r/n))^n)

t = (log_10(A/P)) / (n*log_10(1+(r/n))) = 0,204119/(4*0,006198) = 8,233260

This is the result obtained truncating numbers after the sixth decimal. As for logs, you can use any kind of logs (just be sure to use the same in numerator and denominator). You might want to use log_2 or log_e.
Natural log would be the best way to solve this problem. First rearrange

A/P = (1+r/n)^nt
then apply the nat. log. to get

t = [ln(A/P)] /[n*ln(1+r/n)]

If you do this correctly (please evaluate logs with calculator) you should get

t = 0.874833313

Goodluck
Okay buckle in, here we go!! I had to think back a few years for this, but it was fun. It's also one of those things in algebra that is actually applicable in the "real world."

I will write in the steps as I did them with explanations where needed:

1. 20000 = 12500 (1 + .0575/4)^4t
2. 20000 = 12500 (1.014375)^4t (taking care of parenthetical stuff first)
3. 1.6 = 1.014375^4t (balancing by division of 12500 on both sides)
*** Now we use logarithms and a calulator to find the solution
4. Since LN(1.6) is equal to LN(1.014375)^4t, we also know that:
5. LN(1.6) = 4t LN(1.014375) so we need to get the t by itself by dividing both sides by everything but the t:
6. LN(1.6)/4LN(1.014375) = t
7. On the calc, you have to enter it as follows:
(ln(1.6))/(4ln(1.014375)) and the solution is:
8.2326 (rounded)

Plug in the value of t to check the solution:
12500*(1+(.0575/4))^(4*8.2326) = 20000.015

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