How long will it take a sum of money to triple if it is invested at

10

%

compounded daily? Round to the nearest hundredth of a year.

11.64 years

Step-by-step explanation:

A = P (1+r/n) ^nt

r = interest rate in decimals

t = time in years

n = number of times compounded per year

A = future amount

P = initial amount

We are given that our money will triple so we can let A = 3x if we let P = x

r = 0.1

n = 1

then we can write

3x = x (1 + (0.1/1)) ^1t

3x = x (1.1) ^t

3 = 1.1^t (divide both sides by x)

take log of each side

log 3 = log 1.1^t

log 3 = t*log (1.1)

t = log 3 / log (1.1)

t = 11.64 years