Question

MMS Corp borrows $1,650,000 today for a new building. The loan is an equal principal payment loan with an APR of 6.5% compounded monthly. Payments are due monthly and the term of the loan is 9 years.
The current portion of debt in month 16 is?

Answer 1

Answer:The Current Portion of debt in month 16 is $1461958.53 (rounded off to two decimals)

Explanation:

The question requires us to calculate the balance of the loan in 16 months time. The Balance of the Loan is calculated by taking the loan amount and calculates the Future Value of the amount (in 16 months) and subtract the Future Value of Monthly Loan Payments.

The Monthly Payments were not provided in the question so the first thing we need to do is to calculate monthly payments

Loan Amount = $1650 000

Interest Rate (r) = 6.5/12 .Interest rate is compounded monthly there for the annual Percentage rate of Interest must be divided by 12

Period (N) = 9 years x 12 = 108 months

Monthly Payments Formulae = (r)Loan Amount/(1 -(1 + r)^-n)

Monthly Payments = (0.065/12)1650 000/(1 - (1 + 0.065/12)^-108)

Monthly Payments = 8937.49989/0.4420139495

Monthly Payments = 20219.949846

MMS Corp would pay $20219.949846 for the loan. we will not round of this answer because we want to get an accurate answer wen we calculate Loan Balance (current potion of debt in 16 months time)

Loan Balance (current potion of debt in 16 months time)

Loan Future Value Formulae = Loan Amount (1 + r)^n

Future Value of Monthly Payments = Payments ((1 + r)^n - 1)/r

Current Porting of debt = Loan Amount (1 + r)^n -  Payments ((1 + r)^n - 1)/r

Current Porting of debt = 1650 000(1 + 0.065/12)^16 - 20219.949846((1 + 0.065/12)^16 - 1/(0.065/12)

Current Porting of debt = 1798958.8403 - 337000.31512

Current Porting of debt = 1461958.5252

The Current Portion of debt in month 16 is $1461958.53 (rounded off to two decimals)

Answer 2

Answer:

The current portion of debt in month 16 is $1461958.53  

Explanation:

From the questions given, we thus find the current portion of debt in month 16  

The first step to take  is to calculate the monthly payment  

The Loan /borrowed Amount = $1650 000

The Interest Rate (r) = 6.5/12  

rate is monthly compounded , so the annual Percentage rate of Interest must be divided by 12

The Period (N) = 9 years x 12 = 108 months

The formula for Monthly Payments is:

= (r)Loan Amount/(1 -(1 + r)^-n)

Monthly Payments = (0.065/12)1650 000/ (1 - (1 + 0.065/12)^-108)

Monthly Payments = 8937.49989/0.4420139495

Monthly Payments = 20219.949846

MMS Corp would pay this amount $20219.949846 for the loan.  

In getting the actual answer, we will not round of this answer, we then calculate Loan Balance (current portion of debt in 16 months’ time)

The Loan Balance (current portion of debt in 16 months’ time)

The formula for Loan Future is :

Loan Amount (1 + r)^n

Then,

The  Value of Monthly Payments = Payments ((1 + r)^n - 1)/r

The Current Porting of debt = Loan Amount (1 + r)^n -  Payments ((1 + r)^n - 1)/r

Current Porting of debt = 1650 000(1 + 0.065/12)^16 - 20219.949846((1 + 0.065/12)^16 - 1/(0.065/12)

The Current Portion of debt in month 16 is

So,

Current Porting of debt = 1798958.8403 - 337000.31512

Current Porting of debt = 1461958.5252

Therefore,  The Current Portion of debt in month 16 is $1461958.53