Question

A company has borrowed 1,000,000 from a bank which charges 14 % interest per annum. The loan has to be recovered in 5 years compounded annually

(a) How much should the company pay at the end of each year to the bank (assuming uniform payment)?

(b) The bank changes the interest rate to 13 % p.a . at the beginning of 3rd year

(i) What will the amount of the company's last payment (i.e. payment at the end of year 5) if it keeps on paying the bank the same amount as calculated in (a) above at the end of years 3 and 4?

(ii) What will be the company's repayment schedule if it cñooses to pay back the bank in uniform payments at the end of years 3, 4 and 5?

Tutorial sheet for Lecture 2 (CIVL4013, Macau University) A company has borrowed $1,000,000 from a bank which charges 14% interest per annum. The loan has to be recovered in 5 years compounded annually (a) How much should the company pay at the end of each year to the bankntsi-kse I. (assuming uniform payment)?Yarpynentlo,ooX(UsrT The bank changes the interest rate to 13% pa. at the beginning of 3rd year. (i) What will the amount of the company's last payment (i.e. payment at (b) the end of year 5) if it keeps on paying the bank the same amount as calculated in (a) above at the end of years 3 and 4% 255 (Muscrf) back the bank in uniform payments at the end of years 3, 4 and 5? 253 036,13 (ii) What will be the company's repayment schedule if it cnooses to pay7 2. The construction cost of a sewerage system is estimated to be $30,000,000. The annual operation, maintenance and repair (i.e. OMR) cost will be $1,000,000 per year. The annual income (i.e. benefit) from the collection of sanitation fees from the users will be $3,500,000. Taking a time horizon of 30 years and a discount rate of 5% pa, determine if the project is financially viable 3. Consider the relative costs of a timber pedestrian bridge and a steel one: their

Answer 1

Loan amount=PV=$1,000,000

Number of periods=n=5 years

Rate of interest=i=14%

First we calculate the PV factor of $1 annuity at i=14%, and n=5

a)

Uniform Annual payments=R= PV/PVFa=1000000/3.433081=$291,283.54

b)

i)

Let us see the effect of interest rate change on payment schedule

Year	Principal Amount, P	Interest Rate	Interest, I	Amount=P+I	Paid amount, R	Balance
1	1000000.00	14%	140000.00	1140000.00	291283.54	848716.46
2	848716.46	14%	118820.30	967536.76	291283.54	676253.22
3	676253.22	13%	87912.92	764166.14	291283.54	472882.60
4	472882.60	13%	61474.74	534357.34	291283.54	243073.80
5	243073.80	13%	31599.59	274673.40

Payment should be $274673.40 at the end of 5^th year

ii) Please refer above table, we find that $676,253.22 is left for payment at the end of year 2

Now,

Loan amount left=PV1=$676,253.22

Number of periods=n=3 years

Rate of interest=i=13%

First we calculate the PV factor of $1 annuity at i=13%, and n=3

Uniform Annual payments=R= PV1/PVFa=676253.22/2.361153=$286,408.1