Question

Suppose that you borrowed $400 from a friend and promised to repay the loan by making 3 annual payments of $100 at the end of each of the next 3 years, plus a final payment of $200 at the end of year 4. What is the interest rate implicit in this agreement?

Answer 1

Answer:

The time diagram seem here illustrates the situation.

The interest rate is the rate that will provide a present value of $400 when finding the present value of the $100 three-year ordinary annuity plus the rupees $200 to be received in four years.

The equation involves two unknowns and is not as easily solved as the two previous examples.one way to solve the problem is to trial-and-error the answer.for example if we assumed i to be 9%,the total pv of the payments would be calculated as follows:PV= $100(2.53129)+$200(.70843)=$395.

Because the present value computed is Less than the$400 borrowed, using 9% removes too much interest.recalculating PV with 8% results in a PV of $405. This indicates that the interest rate implicit in the agreement is between 8% and 9%.

The time value of money has many applications in accounting.most of these applications involve the concept of present value.becuase financial instruments typically specify equal periodic payment,these applications quite often involve annuity situations.for example,let's consider one accounting situation using both an ordinary annuity and the present value of a single amount(long-term bonds),one using an annuity due(long term leases) and a third using a differed annuity(pension obligations).