Question

A loan is negotiated with the lender agreeing to accept $8,000 after one year, $9,000 after two years, and $20,000 after four years in full repayment of the loan. The loan is renegotiated so that the borrower makes a single payment of $37,000 at time T and this results in the same total present value of payments when calculated using an annual effective rate of 5%. Estimate T using the method of equated time. Also find T exactly.

Answer 1

Answer and Explanation:

The computation is shown below:

Discount rate 5%  

Year      Cash flow     Discounting cash flows      Cumulative cash flows

0          

1               $8,000         7,619.05                           7,619.05

2               $9,000       8,163.27                              15,782.313

3                                                                                15,782.31

4              $20,000      16,454.05                            32,236.36

PV of loan = 32,236.36

Now

37000 ÷ 1.05^t = 32236.36

t = 2.8248

Discounting cash flows is

= cash flows ÷ (1+rate)^year