Independent solution

How to solve this Dated Deposits and Integer Timing question

Setup

Setup

Use the monthly rate 0.072/12 = 0.006 and express both deposits and the target value on the same date. The unknown n counts months.

j=0.072/12=0.006j=0.072/12=0.006

Model

Model

Solving the equation of value as a real-number equation gives n = 11.73. The stated timing restriction requires the latest completed integer month that still satisfies the condition.

1700(1.006)−n+3400(1.006)−2n=6500(1.006)−601700(1.006)^{-n}+3400(1.006)^{-2n}=6500(1.006)^{-60}

Compute

Compute

Therefore n is 11, not 12.

n=11.73,nmax⁡=11n=11.73,\quad n_{\max}=11

Answer

Answer

The calculation gives 11 for dated deposits and integer timing, matching published choice A.

n=11(A)\boxed{n=11\quad\text{(A)}}