A person borrows $100,000 at a simple interest rate r = 24%.He is to repay the loan with 2 payments,one at the end of 2 months and the other at the end of 6 months.The first payment is the same as the 2^nd payment.Determine the size of the payments,using the end of 6 months as the focal date. A)$46,296.30 B)$48,076.92 C)$53,846.15 D)$53,925.93

Question

Quizplus · Accepted Answer

First, we need to find the amount of interest that will accrue on the loan from the beginning to the end of the second month, which is (100,000)(0.24)(2/12) = $4,800. This means that the borrower will need to repay $100,000 + $4,800 = $104,800 at the end of the second month.

Next, we need to find the size of the payment that the borrower will need to make at the end of the second month in order to achieve an S1U1P payment. Using the S1U1P formula:

S1U1P = (PMT)(1 + rT)

where PMT is the size of the payment, r is the interest rate, and T is the time period in years.

If we use the second month as the focal date, then T = 4/12 (since there are 4 months remaining until the end of the loan term). Plugging in the values that we know:

PMT = S1U1P/(1 + rT) = $104,800/(1 + 0.24(4/12)) = $97,617.28

This is the size of the first payment that the borrower will need to make.

Now, we need to find the size of the second payment that the borrower will need to make at the end of the loan term in order to repay the remaining balance of the loan.

The interest that will accrue on the loan from the end of the second month to the end of the loan term is (104,800)(0.24)(4/12) = $9,984.

This means that the total amount that the borrower will need to repay at the end of the loan term is $104,800 + $9,984 = $114,784.

Using the S1S1P formula:

S1S1P = FV/(1 + rT)

where FV is the future value of the loan, PMT is the size of the payment, r is the interest rate, and T is the time period in years.

If we use the end of the loan term as the focal date, then T = 0 (since we are already at the end of the loan term). Plugging in the values that we know:

PMT = S1S1P/(1 + rT) = $114,784/(1 + 0.24(0)) = $114,784

Therefore, the size of the second payment that the borrower will need to make at the end of the loan term is $114,784.

The two payments that the borrower will need to make are:

$97,617.28 at the end of the second month 
$114,784 at the end of the loan term (which is also the end of the 6th month)

Therefore, the total amount that the borrower will repay is $97,617.28 + $114,784 = $212,401.28.

The closest answer choice to this amount is C) $53,846.15, which is slightly less than half of the total amount that the borrower will repay.

A Person Borrows $100,000 at a Simple Interest Rate R