Simple Interest Problem Ambiguity in Conventions

Question

I am solving some simple interest problems. Following questions are creating ambiguity with conventions, hope someone will clarify what is going on.

1. In what time does sum of money become 4 times at simple interest rate of 10% per annum ?

Here author assumes sum of money is final amount (a) and hence simple interest (si) become Amount(a) - Principal(p) (si = a - p or a = p + si)

2. The simple Interest on sum of money will be 190 after 7 years. In next 7 year principal becomes 3 times, what will be the total interest at the end of the 14^th year ?

Here when author says principal becomes 3 times, according to solutions he means si become 3 times.

Now what is the relation between principal and final amount ? Also isn't principal supposed to be remain constant so how it can becomes 3 times ?

Am i missing something ? Please Help !!!

Answer 1

1) In problem one we are finding the quadrupling time for simple interest:

First, $SI = PRT$ where $P$ is the starting principle, $R$ is the interest rate in decimal, and $T$ is the time in years.

As you have stated, $A = P + SI$. Substituting, it follows that: $A = P + PRT \rightarrow A = P(RT + 1) $

To find the quadrupling time, we can let $A = 4P$, so:

$4P = P(RT + 1) \rightarrow 4 = RT + 1 \rightarrow 3 = RT \rightarrow T=3/R $

So the quadrupling time only depends on the rate. $ 3/.10 = 30. $ Thus, It will take 30 years for the principle to quadruple at 10 percent interest.

2) For problem two. Yes, that is confusing. Princple is constant. You say, they mean "si becomes 3 times". Well, I suppose that means 3 times the principle, not the other way around as you ask.

So in 14 years, $SI = 3P \rightarrow PRT = 3P \rightarrow PR(14) = 3P \rightarrow R = 3/14 \rightarrow R = .2143$

Now, using the information from the first part of the problem, i.e., in 7 years $SI = 190$, then: $ P(.2143)(7) = 190 \rightarrow P = 126.66$

Now, knowing the starting $P$, it is a simple matter to find $SI$ after 14 years:

$SI = (126.66)(.2143)(14) = 380 $

Thus, $380 is earned in interest after 14 years. This is 3 times the starting principle.

Note. I suspect that they might be saying instead, that after 14 years the accummalated amount is 3 times the principle. If so, you would first get an equation for tripling time just like I showed you in problem one, but solve for $R$ instead.

Answer 2

for first 7 years p = 100 % then SI = 190 rs for next 7 years p becomes 3 times = 3(100 %) then SI = 3 (190 rs)

total SI for 14 years is 760 rs.