Question

in how many years will a sum of money become double at 5% p.a?​

Answer 1

Considering the formula for compound interest, which is F=P⋅(1+r)tF=P⋅(1+r)t, where:

FF is the final amount (principal + interest)

PP is the principal (initial value)

rr is the interest rate (5% in your case)

tt is the period of time the interest rate will be applied by (the answer you’re looking for)

So, we just need to work the formula to get to the desired result.

Replacing FF with 2P2P (since in your case the final amount will be double the initial one): 2P=P⋅(1+r)t2P=P⋅(1+r)t

Dividing by PP on both sides: 2=(1+r)t2=(1+r)t

Applying log2log2 on both sides to get ttdown: log22=log2(1+r)tlog2⁡2=log2⁡(1+r)t

Continuing: 1=t⋅log2(1+r)1=t⋅log2⁡(1+r)

Isolating tt: