Algebra homework

Question

You have to choose between three different investment options. Which one is best if you are planning to invest $2500 for 20 years. Option 1 is simple interest at 6% , option 2 is compounding monthly interest at 4% and option 3 is compounding continuously interest at 3.5%

Answer 1

Option 1 will add 6% of $2500 at the end of each year for 20 years. That adds 20($150), or $3000, for a total of $5500.

Option 2 uses the compounding formula P = P₀(1 + r/n)^nt, where P is the final amount, P₀ is the initial amount, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years.

Applying that, we have P = $2500(1 + .04/12)²⁴⁰ = $5556.46

Option 3 uses the continuously compounding formula P = P₀(1+e^rt) = $2500·(1+e^.035·20) = $7534.38