Question

A company buys a machine for $12,000, which it agrees to pay for in five equal annual payments, beginning 1 year after the date of purchase, at an annual interest rate of 4%. Immediately after the second payment, the terms of the agreement changed to allow the balance due to be paid off in a single payment the next year. What is the final single payment (at the end of 3rd year)?

Answer 1

Answer:

Final single payment at the end of third year is $7,779.57

Explanation:

Given:

Present value of machine (PV) = $12,000

Number of annual payments (nper) = 5

Rate = 4% or 0.04

We need to calculate annual payment (pmt). Use spreadsheet function =pmt(rate,nper,PV)

We get, annual payment = $2,695.53

Note: PV is negative as it's a cash outflow.

Payment at made at the end of second year = 2695.53 × 2

                                                                          = $5,391.06

Final payment made at the end of third year = 2695.53 + $\frac{2695.53}{1.04}+\frac{2695.53}{1.04^{2} }$

                                                           = 2695.53 + 2591.86 + 2492.17

                                                           = $7,779.57