Question

Answer the following questions.

1. A company decided to take a 1,000,000 Dhs as a loan from a bank. The negotiations between the company and the bank ended by an agreement stating that the company will take this interest as a compound interest with an interest rate of 6% and that the company will pay equal installments for the next 8 years to return back the loan and its interest to the bank.

a. Determine the annual equal amount of payment by the company to the bank.

b. Determine the total amount of interest the company is going to pay after the 8 years.

c. After the fifth payment (after 5 years) the company had a financial problem and as a result went into a new negotiation with the bank administration which agreed to convert the rest of the amount that was supposed to be paid for the next three years to a pure compound interest loan that can be paid at the end of the three years with the same interest rate of 6% per year.

- What is the new principle for the new loan (P2)?

- What is the amount of money that is going to be paid due to the new loan after the new three years (F2)?

- What is the total amount of interest that is going to be paid after the company fully succeeds to return back the whole loan with its interest? In other words, what is the total amount of interest paid during the 8 years of the loan?

Answer 1

a) To calculate the annual payment we need to solve the following equation:

So the annual payment is 161,035.94

b) Total Interest paid is calculated as follows:

c) To calculate the balance of loan at the end of the 5th year we need to create the amortization schedule:

Year	Opening Balance	Payment	Interest	Principal repayment	Closing Balance
1	1000000.00	161035.94	60000.00	101035.94	898964.06
2	898964.06	161035.94	53937.84	107098.10	791865.96
3	791865.96	161035.94	47511.96	113523.99	678341.97
4	678341.97	161035.94	40700.52	120335.42	558006.55
5	558006.55	161035.94	33480.39	127555.55	430451.00
6	430451.00	161035.94	25827.06	135208.88	295242.12
7	295242.12	161035.94	17714.53	143321.42	151920.70
8	151920.70	161035.94	9115.24	151920.70	0.00
	Total	1288287.54	288287.54	1000000.00

Opening balance = previous year's closing balance
Closing balance = Opening balance+Loan-Principal repayment
Interest = 0.06 x opening balance
Principal repayment = Payment- Interest
So after year 5 the amount of loan remaining is 430,451.00 and this will become the new principal P2

To calculate F2 we need to solve the following equation:

Total interest paid in 8 years = sum of interest on old loan for 1st 5 years + interest on new loan for next 3 years

Total interest paid in 8 years = (60000.00+53937.84+47511.96+40700.52+33480.39)+ (512674.03-430451)

Total interest paid in 8 years = 317,853.74