The Desai Company just borrowed $1,000,000 for 3 years at a quoted rate of 8 percent,quarterly compounding.The loan is to be amortized in end-of-quarter payments over its 3-year life.How much interest (in dollars)will your company have to pay during the second quarter?
A) $15,675.19
B) $18,508.81
C) $21,205.33
D) $24,678.89
E) $28,111.66

Question

Quizplus · Accepted Answer

First, we need to calculate the quarterly interest rate:

i = (1 + r/n)^n - 1 = (1 + 0.08/4)^4 - 1 = 0.0201 or 2.01%

Then, we can use the formula for the quarterly payment:

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

where r is the quarterly interest rate, n is the total number of quarterly payments (12), and A is the loan amount ($1,000,000).

P = (0.0201(1 + 0.0201)^12) / ((1 + 0.0201)^12 - 1) * $1,000,000
P = $35,502.41

The second quarter payment is the same as the first quarter payment, since the loan is amortized over 12 payments:

Payment 1: $35,502.41
Payment 2: $35,502.41 (same as Payment 1)
Payment 3: $35,502.41

Now we can calculate the interest portion of the second quarter payment:

Interest = outstanding balance * quarterly interest rate
Outstanding balance after first payment = $1,000,000 - $35,502.41 = $964,497.59

Interest = $964,497.59 * 0.0201 = $19,407.20

Therefore, the answer is B) $18,508.81.

The Desai Company Just Borrowed $1,000,000 for 3 Years at a Quoted