Compound Interest: a Sequence in Disguise?

A man invested $P in a long term investment plan for 24 years at an interest compounded annually. Due to some financial crisis he had to withdraw money at the end of 6 years. How much more amount could be have gotten after 24 years if he received $3P after 6 years. It is known that there were no other charges of deduction in the plan?

A) 9P

This question is tricky at first since we don’t know the compounding interest rate, and feels like perhaps we would need a compound interest formula to solve, but let’s consider.

It started at P and then compounded 6 times and tripled itself to 3P. So this is more like a Geometric sequence question!

The rule is “P triples every 6 years.”

Year 1 – P
Year 6 – 3P
Year 12 – 9P
Year 18 – 27P
Year 24 – 81P

How much more means we subtract 3P from 81P:
81P-3P = 78P

The answer is (D). This is an interesting question — a sequence in disguise!