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
[tex]P = \frac{r(PV)}{1 - (1+r)^{-n}} , \\ or \\ r(PV) - P[1 - (1+r)^{-n}] = 0[/tex]
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%
