Full question is in description

Question

£500 is invested in a savings account compound intrest is paid at a rate of 5.5% per annum calculate the least number of years it will take for the original investment to double in value.

Answer 1

Hi Armela, the equation to solve is: A = P * (1 + r/n)^nt where:

 

A is the amount plus interest, 1000

P is the amount invested, 500

r is the compounded interest, .055

n is the period, 1 year

t is the time, unknown

 

Substitute:

500 * (1 + .055/1)^1*t = 1000

 

(1.055)^t = 2

 

Change b^y = x to log_b(x) = y

 

(1.055)^t = 2 becomes log_(1.055)(2) = t

 

Change base from 1.055 to 10:

 

t = log₁₀(2) / log₁₀(1.055)

 

t = 12.95 years rounded.

 

Questions?