Problem Solving

varun289 wrote:Joan took out a mortgage from her local bank. Each monthly mortgage payment she makes must be triple the amount of the previous month's payment. If her first payment is $100, and the total amount she must pay back is $328,000, how many months will it take Joan to pay back her mortgage?

This is a geometrical progression problem which requires the formula for the sum of the terms of a geometrical progression. The sum of n consecutive terms of a geometric progression is given by:

• S(n) = a(râ�¿ - 1)/(r - 1), where a is the first term, r is the common ratio of the geometric progression and n = number of terms.

In this case, a = 100, r = 3 and S(n) = 328,000
We need to determine n.

So, 100*(3� - 1)/(3 - 1) = 328000
--> (3� - 1)/2 = 3280
--> (3� - 1) = 6560
--> 3� = 6561

Now, units digit of any power of 3 is 1 only when the power is a multiple of 4.
So, n must be a multiple of 4.
Only option B works.

The correct answer is B.