Amortization (Loans)

[Maximum mark: 6]

In this question give all answers correct to two decimal places.

Stella receives a loan of € $32\hspace{0.15em}000$ for her flower shop business at an interest rate $5.29$ % per year, compounded monthly. She agrees to pay back the loan in $60$ equal installments, made at the end of each month over the next five years.

1. Calculate the amount of monthly installment. [3]
   

Four years after she starts repaying the loan, Stella decides to repay the rest in a final single installment.

2. Calculate the amount owing at the end of the four years. [3]
   

[Maximum mark: 6]

Olivia takes a mortgage (loan) of $\$250\hspace{0.15em}000$ to buy an apartment in Sydney. $\text{Interest}$ on the loan accumulates at the rate of $\$3.49$ % per year, compounded semi-annually. Olivia agrees with the bank to amortise the loan in monthly payments, made at the beginning of each month.

1. Given that the loan is to be amortised over $30$ years, find:

   1. the monthly payment amount;

   2. the total amount paid in amortising the loan. [4]
      

2. Olivia has the capacity to increase her monthly payments by $\$85$. Justify to Olivia why this may be a smart financial choice. [2]
   

[Maximum mark: 5]

Tom takes out a loan of $\$80\hspace{0.15em}000$ to purchase some new machinery for his farming business. He agrees to pay the bank $\$1200$ at the end of every month to amortise the loan. Interest accumulates on the balance at a rate of $5.65$ % per year, compounded monthly.

1. Find the number of years and months it takes to pay back the loan. [2]
   

2. Calculate the total amount that Tom pays in amortising the loan. [1]
   

3. Tom decides to increase the monthly payment to $\$1500$. How much interest will Tom save in comparison to the former payment schedule.[2]
   

[Maximum mark: 7]

Ray takes out a loan of $\$200\hspace{0.15em}000$ to purchase a house. He agrees to pay the bank $\$1250$ at the end of every month to amortise the loan, and interest accumulates on the balance at a rate of $3.79$ % per year, compounded monthly.

1. Find the number of years and months it takes to pay back the loan. [2]
   

2. Calculate the total amount that Ray has paid in amortising the loan. [2]
   

3. Ray decides to increase the monthly payment to $\$1500$. Justify this decision.[3]