Investment/Interest Question

Question

An investrnent of $300,000 which earns interest at the

rate of 15 percent per year is rnade. If the interest is

compounded continuously, (a) What will the investrnent

grow to if it is invested for 35 years? (b) 47 years?

(c) How long is required for the investrnent to increase by 175 percent?

Answer 1

Continuous compound interest is given by Aeʳᵗ where A is the amount, r the annual rate and t the time in years. So A=300000 and r=0.15.

(a) t=35: 300000e⁵˙²⁵=$57,169,880.54

(b) t=47: 300000e⁷˙⁰⁵=$345,857,622.80

(c) An increase of 1.75 is a growth of 2.75, which is 825000/300000.

e⁰˙¹⁵ᵗ=2.75, t=ln(2.75)/0.15=6.744 years approx.