Answer to Question #205406 in Financial Math for Samkelisiwe Ndwala

Question

Zodwa needs R450 550,00 to buy a house. The bank approved her loan for the full amount at an interest rate of 25% per year, compounded quarterly. The loan must be paid off in ten years’ time. Question 13 Determine the size of Zodwa’s quarterly payment

Question 14 What will the outstanding balance on Zodwa’s loan be at the end of seven years if the interest rate remains unchanged? 

Answer 1

To find the quarterly payments, we will use the 'PMT' function in excel.

note that we have taken 40 for number of periods (10 years $\times$ 4 quarters per year). Have taken interest rate quarterly too (25% / 4 = 6.25%). Loan amount is Present Value and Future value will be 0 as we want to payoff the loan by the end of 40th quarter.

Now if we solve for PMT, we will get 3,089,275.

Thus, quarterly payment is $3,089,275.

To find the balance after 7 years, we will have create an amortization schedule.

Amortization schedule simply shows the outstanding balance of loan after every period. 

1st column is the number of year. 2nd column is for number of quarter as out payments are quarterly.

3rd column is for beginning balance of loan for a particular period.

4th column is our installment for every quarter.

5th column is Interest paid on the beginning balance, for that we will simply multiply the beginning balance with the interest rate (45,055,000 * 0.0625 for the first period)

6th column is the principle amount paid, which is simply the difference between the payment and interest paid.

7th column is for the ending balance of loan for a particular period. Ending balance is found as, Beginning balance - principle payment = Ending balance. Every period's ending balance will be next period's opening balance.

Now, as we can see from the table in step-2, outstanding balance of loan after 7 years will be 25,548,676 that is ending balance of quarter number 28.

Thus, outstanding balance on Zodwa’s loan be at the end of seven years is R25,548,676.