INT Practice Questions

1. The investment contract guarantees to make three interest payments:

\(\$10,000\) (initial investment) \(+ \$200\) (\(1\%\) interest on \(\$10,000\) principal \(= \$100\), so \(2\% = 2 \times \$100\))

\(\$10,200 + \$306\) (\(1\%\) interest on \(\$10,200\) principal \(= \$102\), so \(3\% = 3 \times \$102\))

\(\$10,506 + \$420.24\) (\(1\%\) interest on \(\$10,506\) principal \(= \$105.06\), so \(4\% = 4 \times \$105.06\))

\(\$10,926.24\)

The final value is \(\$10,926.24\) after an initial investment of \(\$10,000\). Thus, the total amount of interest paid is \(\$926.24\) (the difference between the final value and the amount invested).

The correct answer is E.

In this question, interest is accruing on previous interest (because interest payments are being reinvested into the contract). We are not being able to use a standard CI amount formula here because we don't have one fixed rate to compound

Initial investment \(= 10,000\)
Interest paid at the end of \(6\) months \(= 200\)
Amount at that point of time becomes \(10,200\)

At the end of \(12\) months, interest will be calculated at \(3\%\) of this previous amount. Hence interest \(= 306\)
Amount at that point in time becomes \(10,506\) and this is the amount on which \(4\%\) interest will be paid at the end of \(18\) months

Then interest paid at the end of \(18\) months \(= 420.24\) and amount becomes \(10,926.24\)

Initial investment was \(10,000\), then total interest paid out was \(926.24\)

The correct answer is E.

If we decide to find a constant multiple by the hour, then we can say that the population was multiplied by a certain number three times from 1 p.m. to 4 p.m.: once from 1 to 2 p.m., again from 2 to 3 p.m., and finally from 3 to 4 p.m.

Let's call the constant multiple x.

\( 2000(x)(x)(x) = 250,000 \)
\( 2000(x^3) = 250,000 \)
\( x^3 = \frac{250,000}{2,000} = 125 \)
\( x = 5 \)

Therefore, the population gets five times bigger each hour.
At 3 p.m., there were \( 2000(5)(5) = 50,000 \) bacteria.

The correct answer is A.

Formula:
Nth term of GP is given by = (first term) ((Ratio^n)-1) or an=a1R(n−1)
Pure calculation:
The stem says that it doubles every 2 hours. We know that 4 hours ago their number was 1000. So, we add - 4 hours and the number 1000. In 2 hours, their number doubles, so we add - 2 hours and the number 2000. Using the same logic, their number is now
2000*2= 4000. We continue by adding hours to now, so now+2, now+4, now+6.....

When we reach to + 12 their number is 256000, which is more than 250000, and we can stop!
4 hours ago: 1,000
2 hours ago: 2,000
Now: 4,000
In 2 hours: 8,000 in 4 hours: 16,000 in 6 hours: 32,000 in 8 hours: 64,000 in 10 hours: 128,000 in 12 hours: 256,000

Or using formula: a1 is the first term and then an=a1R(n−1), which is the term in the nth place.
Between the first term and the nth term, n−1 multiplications by the ratio R take place, and this is reflected in the exponent of n−1.
Using the formula, you deduced that if a1=4000 is the first term, then the 7th term will be greater than 250,000. Between the first population and the 7th one, 6 cycles of 2 hours passed, a total of 12 hours, which is the correct answer.

The correct answer is D.