Problema Solution
Suppose $5,200 is invested in an account at an annual interest rate of 6.3% compounded continuously. How long ( to the nearest tenth of a year) will it take the investment to double in size?
Answer provided by our tutors
double in size gives a value 10,400
rate 6.3 is "0.063" as a decimal
the formula we use for compounding interest is:
T=P(1+r/n)^(nt)
where 'T' is the total (10,400), 'P' is the principal (5,200), 'r' is the rate (0.063), 'n' is the number of times a compounding is applied ('1' for an annual compounding), and 't' is the time (in years) it takes for the investment to have doubled
10400 = 5200(1+0.063)^t
t=11.34
So it would take approximately 11.3 years for the original investment to double.