## Question

###### (2 points) Brandon and Kayla have decided to borrow $17,100 to buy a new Honda Fit....

- (2 points) Brandon and Kayla have decided to borrow $17,100 to buy a new Honda Fit. They were able to obtain a 5-year loan with an interest rate of 4.5%. Find their monthly payment.
- (2 points) Brandon and Kayla owe $36,000 on their student loans at an interest rate of 7%. The term is 20 years. Find their monthly payment.
- (1 point) Construct the first row of the amortization table for their student loans.

How much of their first payment goes toward interest?

How much of their first payment goes toward principal?

After making their first payment, what is the remaining balance? - (1 point) Construct the second row of the amortization table for their student loans.

How much of their second payment goes toward interest?

How much of their second payment goes toward principal?

After making their second payment, what is the remaining balance? - (2 points) Continue constructing the amortization table for their student loans until you have completed 12 rows of the table. What is the total amount of interest that Brandon and Kayla will pay on their student loans in the first year?
- (2 points) Explain how you constructed the amortization table for their student loans. Include all of the formulas that you used. Show your calculations for at least one row of the table.

## Answers

Monthly payments of Car Loan=

$318.80as follows:Monthly payments of Student Loan=

$279.11as follows:Amortization schedule of the student loan for the first year (12 months) is as follows:

How much of their first payment goes toward interest? Answer:

$210

How much of their first payment goes toward principal? Answer:$69.11After making their first payment, what is the remaining balance? Answer:

$35,930.89How much of their second payment goes toward interest? Answer:

$209.60

How much of their second payment goes toward principal? Answer:$69.51

After making their second payment, what is the remaining balance?:Answer:$35,861.38Total amount of interest to be paid on Student loan in the first year=

$2,492.87Method of constructing amortization schedule:

1. Loan amount is the beginning balance of the entire term as well as the first payment period (month)

2. Monthly interest rate is calculated by dividing the yearly interest rate by 12. In the given case, monthly interest rate= 7%/12= 0.00583333

3. Interest for each month is calculated by multiplying the beginning balance by monthly interest rate. In the given case, interest for first month= $36,000*0.00583333= $210

4. Principal component of each monthly payment is calculated by deducting the interest for that month from the monthly payment. In the given case, principal component of first month payment= $279.11- $210 = $69.11

5. End balance of each month = Beginning balance minus principal repaid during that month. The end balance of each month will be the beginning balance of the succeeding month.

In the given case, end balance of the first month= $36,000 - $69.11 = $35,930.89

в со 1 Monthly payments of fixed rate loan. 2 Payments at the end of each month 3 Monthly payments (PMT) is calculated using the formula EMI=[P*r*(1+r)^n]/[(1+r)^n)-1 4 Where P= Principal (loan amount), 5 n= Number of installments. ie if N= number of years, n=N*12 6 r= Rate of interest per month in decimals ie. If R= Yearly rate, r=R/(100*12) All amounts in $ 8 Given that 9 Principal (loan amount) (P)= 100 No. of years (N)= 10 Rate of interest (% p.a)=R= 4.5 No. of months (n)= 60 11 12 Calculations: 13 14 Interest rate per month in decimals (r )= 15 No. of months (n)= 16 60 Formula Cell reference Value R/(100*12) D10/(100*12) 0.00375 N*12 G9*12 (1+r)= 1+G14 1.00375 (1+r)^n= G16^G10 1.25179582 [(1+r)^n]-1= G17-1 0.25179582 P*r*(1+r)^n= D9*G14*G17 80.271407 [P*r*(1+r)^n]/[(1+r)^n)-1 G19/618 318.795629 Rounded to $ 318.80 18 19 20 Monthly payments (PMT)= 21 22A B C D E F 1 Monthly payments of fixed rate loan. Payments at the end of each month 3 Monthly payments (PMT) is calculated using the formula EMI=[P*r*(1+r)^n]/[(1+r)^n]-1 4 Where P= Principal (loan amount), 5 n= Number of installments. ie if N= number of years, n=N*12 6 r= Rate of interest per month in decimals ie. If R= Yearly rate, r=R/(100*12) All amounts in $ Given that 9 Principal (loan amount) (P)= 36,000 No. of years (N)= 10 Rate of interest (% p.a)=R= 7 No. of months (n)= 20 240 11 12 Calculations: 13 14 Interest rate per month in decimals (r = 15 No. of months (n)= 16 11 Formula Cell reference Value R/(100*12) D10/(100*12) 0.00583333 N*12 G9*12 240 (1+r)= 1+G14 1.00583333 (1+r)^n= G164G10 4.03873885 [(1+r)^n)-1= G17-1 3.03873885 P*r*(1+r)^n= D9*G14*617 848.135158 [P*r*(1+r)^n]/[(1+r)^n]-1 G19/618 279.107617 Rounded to $ 279.11 18 19 20 Monthly payments (PMT)= 22