Question

I put $500 in the bank. I now have $5000in the bank. Every year my money increased by 5%. How long that it takes?

Answer 1

Answer:

It takes 47.19 years

Step-by-step explanation:

Your amount on the bank is given by the following equation:

$P(t) = P(0)(1+r)^{t}$

In which P(t) is your current amount, P(0) is the initial amount, r is the rate it changes, and t is the time since the money has been put on the bank.

I put $500 in the bank.

This means that $P(0) = 500$

I now have $5000 in the bank.

This means that $P(t) = 5000$

Every year my money increased by 5%

This means that $r = 0.05$

How long that it takes?

This is t.

$P(t) = P(0)(1+r)^{t}$

$5000 = 500(1.05)^{t}$

$(1.05)^{t} = \frac{5000}{500}$

$(1.05)^{t} = 10$

$\log{(1.05)^{t}} = \log{10}$

We use the following logarithms property:

$\log{a^{t}} = t\log{a}$

So

$t\log{1.05} = \log{10}$

$t = \frac{\log{10}}{\log{1.05}}$

$t = 47.19$

It takes 47.19 years