An investment earns interest that is compounded continuously
MATHEMATICS · Multi-part · AP · AP Precalculus · Exponential and Logarithmic Functions · Exponential and Logarithmic Functions
Problem
An investment earns interest that is compounded continuously. Its value reaches ₹1,50,000 two years after the initial deposit and ₹2,70,000 five years after the deposit.
(i) Determine the continuous annual growth rate r (expressed as a percentage correct to two decimal places).
(ii) Find, correct to one decimal place, the time (in years from the initial deposit) required for the investment to triple in value.
(iii) Derive a general formula for the time T (in terms of r) needed for the investment to reach any multiple m>1 of its initial value.