need some finance help please?
1. Your neighbor is buying a new recreational vehicle (RV). He has the following options to finance the RV:
I. Pays $42,000 today (in time 0)
II. Buy under a “no payments for two years” program by agreeing to pay $45,000 two years from today (in time 2).
III. Make 72 monthly payments over 6 years of $675 payable at the end of each month.
A) If the interest rate is 7% annually, calculate the present value of each option.
I) 42,000/(1.07)^0=42,000
II) 45,000/(1.07)^2=39304.74
(72*675=48600
III) 48600/(1.07)^6=32384.23
(b) How low does the interest rate have to fall before Option I is a better deal than Option II?
3% 45,000/(1.03)^2=42416.82
What’s your question?
Option III requires a monthly interest rate ( 7% / 12, or .00583%per month) for 72months. My calculation of the PV of an Annuity of $675, at 7% compounded monthy = $39,596.
Under Option II, paying $45,000 in 2 years at 3.51% gives a PV of $42,000.