Assignment 1

1. How much money can you borrow now if you repay the lender Rs. 850 in 2

years and the interest rate is 6% compounded yearly?

2. If you invest Rs. 10,000 now in a business venture that promises to return Rs.

14,641, how soon must you receive the Rs. 14,641 in order to make at least a

10% per year return compounded annually on your investment?

3. Your uncle has agreed to make five Rs. 700 per year deposits into a savings

account for you starting now. You have in turn agreed not to withdraw any

money until the end of year 9, at which time you plan to remove Rs. 3000

from the account. Further, you plan to withdraw the remaining amount in 3

equal year-end installments after the initial withdrawal. Diagram the cash

flows for your uncle and for yourself. Interest rate is 8%.

4. If you invest Rs. 4100 now and receive Rs. 7500 five years from now, what is

the rate of return on your investment? Define the economy symbols and

construct the cash-flow diagram

5. How much money would be accumulated in 6 years if a person deposited Rs.

500 now and the deposits increase by Rs. 50 per year for the next 6 years?

Assume ‘i’ is 16% per year and draw the cash-flow diagram.

6. A company is planning to make 2 equal deposits such that 10 years from now,

the company will have Rs. 49,000 to replace a small machine. If the first

deposit is to be made 2 years from now and the second is to be made 8 years

from now, how much must be deposited each time if the interest rate is 15%

per year?

7. If a college student can save Rs. 600 per year from her part-time job, how long

will it take her to save enough money to purchase a Rs. 2,500 bicycle if she

can get 10% per year interest on her money?

8. For the cash flow below, calculate (a) the equivalent uniform annual cost in

years 1 through 5 and (b) the present worth of the cash flow. Assume that the

interest rate is 12% per year.

Year 1 2 3 4 5

Cash Flow (Rs.) 5000 5400 5800 6200 6600

9. For the diagram shown below, find the value of ‘x’ that will make the negative

cash flows equal to the positive cash flow of Rs. 800 at time 0. Assume that

i=15% per year.

100 150

200 X?

1 2 3 4

Year

Rs. 800

10. A company borrows Rs. 15,000 at an interest rate of 15% per year with the

agreement that the loan will be repaid over an 8 year period. The repayment

scheme will be such that each payment will be Rs. 250 larger than the

preceding one, with the first payment to be made 1 year after the loan is

negotiated. Determine the amount of the third payment.

11. Assume that a company wants to have Rs. 5,00,000 available for investment

10 years from now. The company plans to invest Rs. 4,000 the first year, and

amounts increasing by a uniform gradient thereafter. If the company’s interest

rate is 20% per year, what must be the size of the gradient in order for the

company to meet its objective?

12. A businessman purchased an existing building and found that the ceiling was

poorly insulated. He estimated that with 6 inches of foam insulation, he could

cut the heating bill by Rs. 25 per month and the air-conditioning cost by Rs.

20 per month. Assuming that the winter season is the first 6 months of the year

and the summer season is the next 6 months, how much can he afford to spend

on insulation if he expects to keep the building for only 2 years? i= 1.5% per

month?

13. A woman plans to make a total of 8 deposits, with the first deposit now and

succeeding deposits at 1-year intervals, so that she will be able to withdraw

Rs. 4000 per year for the next 10 years, the first withdrawal starting 16 years

from now. How much must she deposit each year if the interest rate is a

nominal 12% per year compounded quarterly?

14. If a machine costs Rs. 15,000 to purchase and the operating costs are Rs. 1000

at the end of the first year, Rs. 1200 at the end of the second and amounts

increasing by Rs. 200 per year through year 12, what is the present worth of

the machine if the interest rate is a nominal 15% per year compounded semi-

annually?

15. If a company can buy an equipment for Rs. 6,00,000 with the expectation of

spending Rs. 48,000 per year for operation and maintenance, how much could

it afford to spend on a new one if its annual cost would be only Rs. 38,000 per

year? Assume that the salvage values will be 10% of the first cost and that

both machines will have a 5 year life. Use i=15% and f=10% per year.