Suppose I have 2 options for how to pay for something: A: I can be $2,977 right

Question

Suppose I have 2 options for how to pay for something:

A: I can be $2,977 right now
or
B: I can pay $395.25 for 8 consecutive months, for a total of $3,162

I will now clarify in more detail what I mean by option B.

Suppose the date is January first. Choosing option B means giving the seller 8 checks, each one being for $395.25

The first check would be dated February 1st, the next one would be dated March first, then April first, etc. until we get to the last check (the eighth one), which is dated September first.

If I chose option A, I would be losing $2,977. If I chose option B, I would lose more than that, but the loss would be spread over time.

What is the effective monthly interest rate I would be paying if I chose option B? In other words, what interest rate would make $2,977 be equivalent to the 8 monthly payments I mentioned above?

I know the answer is supposed to be 1.36%

Please explain how to arrive at this answer. Thank you.

Explanation / Answer

OPTION B : let monthly rate be k. THIS OPTION WILL BE EQUAL TO OPTION A, IF PV OF CASH FLOWS IN OPTION B IS EQUAL TO AMOUNT OF OPTION A. PV of B = 2977 = 395.25((1+k)^8-1)/(k(1+k)^8) at k= 0.014, RHS = 2971 ($) at k =0.013, RHS = 2984.8 ($) so k = 0.0136, RHS = 2976.9 almost = 2977($) Hence, k = 0.0136 = 1.36% (ANSWER)

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