The ABC company lends $A to a person who agrees to pay back $500 at the end of every three months for two years.ABC estimates there is a 2% chance this person will default on a payment.If the interest rate on the loan is j₄ = 6%,what should be the value of A? A)$3668.10 B)$3737.98 C)$3742.96 D)$3747.76

Question

Quizplus · Accepted Answer

First, we need to calculate the total amount that the person will pay back over the two years:

$500 x 8 = $4000

However, since there is a 2% chance of default, we need to adjust for that by multiplying by 98%:

$4000 x 0.98 = $3920

We can now use the formula for present value of an annuity to find the initial amount lent (A):

A = P * (1 - (1+i)^(-n)) / i

where P is the periodic payment ($500), i is the interest rate per period (6%/4 = 1.5%) and n is the total number of periods (8).

A = $500 * (1 - (1+0.015)^(-8)) / 0.015
A = $3737.98

Therefore, the best choice is B.

The ABC Company Lends $A to a Person Who Agrees