Interest compounded annually

[adonai]

If $4000 is deposited into an account paying 3% interest compounded annually and at the same time $2000 is deposited into an account paying 5% interest compounded annually, after how long will the two accounts have the same balance? Round to the nearest year and show all work.
I know that we are supposed to use the formula for compounding interest annually, A = P(1+r/n)[sup:2ai33udf]nt[/sup:2ai33udf], but I really do not know how to progress from there. :?:

 

[stapel]

I know that we are supposed to use the formula for compounding interest annually, A = P(1+r/n)[sup:28jlhpk8]nt[/sup:28jlhpk8], but I really do not know how to progress from there.

You are given two principal amounts. In the compound-interest formula, which variable stands for the principal?

You are given two interest rates. Which variable stands for the interest rate?

You are given the same compounding frequency for each account. Which variable stands for the compounding frequency?

Plug the values into the formula for the appropriate variables. This gives you two expressions, one for each account, for the amount in the accounts after some time period t.

You are asked when the amounts are equal. Set the expressions equal to each other, and solve for the time t.

If you get stuck, please reply with a clear listing of your steps so far. Thank you!

Eliz.

 

[adonai]

Allright, I have 4000(1+.03/1)[sup:h19dmwnp]1t[/sup:h19dmwnp]=2000(1+.05/1)[sup:h19dmwnp]1t[/sup:h19dmwnp]. How do I solve for t?

 

[skeeter]

4000(1.03)[sup:159ymvx2]t[/sup:159ymvx2] = 2000(1.05)[sup:159ymvx2]t[/sup:159ymvx2]

divide both sides by 2000 ...

2(1.03)[sup:159ymvx2]t[/sup:159ymvx2] = (1.05)[sup:159ymvx2]t[/sup:159ymvx2]

divide both sides by (1.03)[sup:159ymvx2]t[/sup:159ymvx2] ...

2 = (1.05/1.03)[sup:159ymvx2]t[/sup:159ymvx2]

take the log of both sides and use the power property of logs ...

log(2) = t*log(1.05/1.03)

t = log(2)/log(1.05/1.03) = a smidge over 36 years