Interest Rates

A loan has a variable interest rate that fluctuates between 5% and 9% of the base payment per month. If base payments remain at $250 each month and an additional monthly surcharge of 1% is added to the combined (base + interest), what would be the greatest possible payment due in any given month?
A. $ 262.50
B. $ 265.13
C. $ 272.50
D. $ 275.23
E. $ 286.13

OA is D

This question looks unfamiliar, what is the best possible approach to solving this? An Expert is urgently needed.

Hi Roland2rule,
Let's take a look at your question.

To find the greatest possible value in the given month, we will be using the greatest interest rate i.e. 9%.
Base payment = $250
$$\text{Interest on base payment}\ =\ 250\times9\%$$
$$\text{Interest on base payment}\ =\ 250\times\frac{9}{100}=22.5$$
$$\text{Total payment after 9% interest}=250+22.5=272.5$$

An additional monthly surcharge of 1% is added to combined (base+interest).
Let's first calculate the amount of additional monthly surcharge on total payment.
$$\text{Additional Monthly surcharge}\ =272.5\times1\%$$
$$\text{Additional Monthly surcharge}\ =272.5\times\frac{1}{100}=2.725$$

$$\text{Greatest possible payment due}\ =272.5+2.725$$
$$\text{Greatest possible payment due}\ =275.225\approx275.23$$

Therefore, Option D is correct.

Hope it helps.
I am available if you'd like any follow up.