What would the annual rate of interest have to be?

Question

Chester hopes to earn
$1200
in interest in
3.3
years time from
$96,000
that he has available to invest. To decide if it's feasible to do this by investing in an account that compounds daily, he needs to determine the annual interest rate such an account would have to offer for him to meet his goal.

Answer 1

It should be sufficient to use the formula for continuous compounding because the difference between it and daily compounding is trivial.

 

A = Pe^rt with A = 97,200 (original P + interest), P = 96,000, t=3.3.  SOLVE for r.

 

Hints: first, divide both sides of equation by P; then ln (A/P)= rt. You know t; solve for r.  Carry out all calculations to as many dec. places as your calculator can provide. In the end, to state r, use four or five decimal places, rounded up, and that will be sufficient.