Question

An unknown capital gets added 5% interest per year by a bank. After how many years does the capital get three times as big, considering compound interest? Doesn't necessarily need to be the final answer, I just need to know how to start please. ​

Answer 1

After 23 years , the capital will get three times as big

Explanation:

Firstly, let us write the compound interest formula

P = I( 1 + r)^n

Since we are considering a capital rise of 3 times

If I, the initial value is x, the P

value later will be 3x

Interest rate is 5/100 = 0.05

so we need the value of t

This will be;

3x = x(1 + 0.05)^t

3= 1.05^t

ln 3 = t ln 1.05

t = ln 3/ln 1.05

t = 23 years