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your business has just taken out a 1-year installment loan for $72,500 at a nominal rate of 11.0% but with equal end-of-month payments. what percentage of the 2nd monthly payment will go toward the repayment of principal? a. 77.55% b. 90.45% c. 81.63% d. 85.93% e. 73.67%

1 Answer

5 votes

Answer:

90.45%

Step-by-step explanation:

We will be solving this problem by using a formula that gives us the monthly payment installments on a loan, with other supporting equations.

We are given,

Principal = $72,500

Nominal Rate = 11.0%

Duration = 1 year

The monthly interest rate can be calculated as follows.

Monthly Interest = (11 /12) = 0.917%

For calculating equal installment payments on the loan, we use

Installment Amount = Principal / Present V. A Factor

V.A - Value Annuity

Present V.A = (1 - (1 + r)^(-n)) / r

where

r = monthly interest rate

n = number of payments

For the 1-year duration mentioned in the question, the number of total payments would be 12.

Thus, the present V.A would be

Present V.A Factor = (1 - (1 + 0.00917)^(-12)) / 0.00917

Present V.A Factor = 10.63

Therefore, the monthly installment amount is:

Installment amount = 72,500 / 10.63

Installment amount = $6,820.31

Finding a portion of the second monthly payment allocated,

Interest portion = Principal * Interest rate

Interest portion = 72,500 * 0.00917

Interest portion = $665.22

The principal portion of the second-month payment is

$6,820.31 - $665.22 = $6,155.09.

Percentage of 2nd monthly payment for principal = (6,155.09 / 6,820.31) * 100

Percentage of 2nd monthly payment for principal = 90.45%

Therefore, the percentage of the 2nd Monthly payment which goes towards loan repayment will be 90.45%

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