General Annuity practice question

Question

I'm taking an introductory course in finance but I don't understand how to do this question:

A used car may be purchased for 7600 cash or 600 down and 20 monthly payments of 400 each,the first payment to be made in 6 months. What annual effective rate of interest does the installment plan use?

What I tried to do was equate the 7600 to the discounted value of the monthly payments, plus the 600, but I'm not sure how to solve for 'i'. This is the equation I have now: 7600 = 400 x [1-(1+i)^-20]/i + 600

What expression do you have for the discounted value of the payments? It should be a geometric series that you can sum. — Ross Millikan, Mar 06 '19 at 20:55
Right now I have an equation like this: 7600 = 400 x [1-(1+i)^-20]/i + 600 — Kaladin Stormblessed, Mar 06 '19 at 20:56
I don't see it in the comment. You should edit it into the question to show what you have tried and where you are stuck — Ross Millikan, Mar 06 '19 at 20:59
You do realize that you are not required to solve for i algebraically since it is a degree 20 equation. You will probably be using some table/calculator to get i. — Matthew Liu, Mar 06 '19 at 21:27

score 1 · Answer 1 · answered Mar 06 '19 at 21:24

You have not taken account of the delay in receiving payments. There should be another factor $(1+i)^{-5}$ to take account of the five months with no payments. Then solving for $i$ requires a numeric approach. A spreadsheet will do it for you or you can use bisection. $i=0$ is too low and you can easily find an $i$ that is too high. Then compute it at the center point and see if it is too low or too high.

score -2 · Answer 2 · edited Mar 06 '19 at 23:58

-2

Start by letting $i$ be the monthly interest rate, not the annual rate. The answer to the question will be $(1+i)^{12} - 1$

edited Mar 06 '19 at 23:58

dantopa

10,342

answered Mar 06 '19 at 21:32

Justin

5
3

Welcome to Mathematics Stack Exchange! A quick tour will enhance your experience. Here are helpful tips to write a good question and write a good answer. For equations, please use MathJax. – dantopa Mar 06 '19 at 23:58

General Annuity practice question

2 Answers2

Linked