Question

How long will it take money to double if it is invested at 6​% compounded monthly? 5.3% compounded​ continuously?

Answer 1

At 6% compounding monthly:-

If we invest $1 for n periods at 6% compounding monthly then we get $2 after n periods.

2 = 1 × ( 1 + 0.06/12)^{n ×12}

2 = ( 1+ 0.005)¹²ⁿ

Apply log on both sides

Log 2 = 12n log 1.005

12n = log 2 / log 1.005

12n = 138.975721611

n = 138.975721611 / 12

n = 11.5813101343

If you invest at 6% compounding monthly then it will take to double is 11.58 years

At 5.3% compounding continuously :-

2 = 1 × e^r×n

2 = e^{0.053 × n}

Apply log

Log 2 = 0.053n log e

0.053n = log 2/ log e

0.053 n = 0.6931471805

n = 0.6931471805 / 0.053

n = 13.0782486887

If you invest at 5.3% compounding continuously then it will take to double is 13.08 years