Question

You borrow $245,000; the annual loan payments are $23,847.41 for 30 years. What interest rate are you being charged? Round your answer to two decimal places.

Answer 1

PV of annuity for making pthly payment
P = PMT x (((1-(1 + r) ^- n)) / i)
Where:
P = the present value of an annuity stream
PMT = the dollar amount of each annuity payment
r = the effective interest rate (also known as the discount rate)
i=nominal Interest rate
n = the number of periods in which payments will be made
Loan	245000
Annual payment	23847.41
Time in years	30
Assumed Interest rate	10%
Assumed Interest rate	8%
PV	= 23847.41* (((1-(1 + 8%) ^- 30)) / 8%)
PV @ 8%	268,468.98
NPV @ 8%	23,468.98
PV	= 23847.41* (((1-(1 + 10%) ^- 30)) / 10%)
PV @ 10%	224807.4943
NPV @ 10%	(20,192.51)
IRR	=Lower rate + Difference in rates*(NPV at lower rate)/(Lower rate NPV-Higher rate NPV)
IRR=	=8%+(10%-8%)*((23468.98/(23468.98+20192.51))
IRR=	9.075%