Question

​d'anthony borrowed​ $50,000 today that he must repay in 15 annual endminus−ofminus−year installments of​ $5,000. what annual interest rate is​ d'anthony paying on his​ loan?

Answer 1

Given:
Amount of the loan, PV = $50,000
Number of payment periods, n = 15
Yearly payment, P = $5,000

Let r = annual interest rate.
Then

`P = (r(PV))/(1 - (1+r)^(-n)) , \\ or \\ r(PV) - P[1 - (1+r)^(-n)] = 0`

Insert given information into this equation to obtain
50000r - 5000[1 - (1+r)⁻¹⁵] = 0

Write the equation as
f(r) = 10r + (1+r)⁻¹⁵ - 1 = 0

-- r - f(r)
-------- ----------
0.010 -0.039
0.020 -0.057
0.035 -0.053
0.045 -0.033
0.055 -0.002
0.060 0.017

The solution is obtained graphically (see the accompanying figure) as
r = 0.055 = 5.5%

Answer: The annual interest rate is 5.5%