How long will it take for a lump-sum investment to triple in value at an interest rate of 1.5% per six-months, compounded continuously?

Answer 1

Hello Nicholas,

you can use this formula for compounded interest: Y= C * (1+p/100)^(x/T)

C is the capital or lump-sum that you wish to invest.

p is the interest rate in percent .

x is the time that has passed since investing

T is the period; this is the time it takes for your interest rate . In your example 1.5% per six months.

So your T =6 x is the number you are looking for and since you want your investment to tripple

C can remain C

and y= 3*C

X and T must be the same unit. So if you have months for T, X must also be in months. (Unless you change the formula accordingly)

So for your case the formula looks like this

3*C = C* (1+1.5/100)^(m/6) | divide by c

3 = (1.015)^(m/6) | apply a log to solve for exponent

log_1.0153 = m/6 | multiply with 6

m = (log _1.015 3) * 6

m= 442.7 months

If your calculator doesn't have a button for the log like it is written above you can calculate the value like this:

m = (log3 / log1.015) * 6

Of course this will give you the same result.

Feel free to get in touch if you have any questions about this solution.