Question

12. A 100,000 loan is repaid by 14 annual payments of 4,750 at the end of each year and a single payment of 104,900 at the end of the 14th year. Compute the effective annoal rate of the loan. (5%)

I am taking a financial institutions and markets course and most of the exercises I solve with my TI 84 Plus (texas instruments) using either the TVM solver or the other Financial apps such as bal( or ΣPrn( or ΣInt(. However, for some, I don't know how to and, even though there are answers, I can't fully understand them because of the annuity symbol (the angle mark that is on the solution below). My problem is that I don't understand what that means mathematically and I cannot proceed with the calculations. I searched all around for some explanation and I could not find any, maybe it is a very simple problem and I hope someone can explain it to me.

Answer 1

The annuity symbol means that a uniform cash flow of 4750 paid for 14 years and we have to find its present value discounted at interest rate r.

Similarly PV of 104900 paid at end of 14 years = 104900/(1+r)^14

So the equation to be solved is 100000 = 104900/(1+r)^14 + 4750*(1/(1+r) + 1/(1+r)^2 +.....+ 1/(1+r)^14)

Solving this equation in a spreadsheet we get r = 5%