Expert: Scott A Wilson - 2/2/2011

Question
How do you solve this scenario and which one would you chose

Scenario A: invest 5000 at 6.5 % compounded quarterly until you reach 10000

Scenario B: invest 5000 at 6.5% compounded annually until you reach 10000

Answer
A: Since 6.5% is compounded quarterly, the interest per quarter is 6.5/4 = 1.625%.
That answer is n where 1.625^n = 10000/5000 = 2.
So, n ln(1.01625) = ln(2), for which I get n = 43, so time is 10 years, 7 months.

B: This one would take a little longer since the interest isn't broken down to quarters.
The answer gives the equation n ln(1.065) = ln(2), so n = ln(2)/ln(1.065).
The answer is 11 years.