3. Your neighbor is buying a new recreational vehicle (RV). He has the following

Question

3. Your neighbor is buying a new recreational vehicle (RV). He has the following options to finance the RV:

                        I. Pays $60,000 today (in time 0)

                        II. Buy under a "no payments for three years" program by agreeing to pay                                     $70,000 three years from today (in time 3).

                        III. Make 84 monthly payments over 7 years of $850 payable at the end of                                   each month.

            (a) If the interest rate is 6% annually, calculate the present value of each option.

(b) At what interest rate do Option II and Option III have the same present value?

Explanation / Answer

(a)

Option 1: Present Value = $60,000

Option 2: Present Value = 70,000 x PVF(6%, 3 years) = 70,000 x 8.8396 = $58,773.35

Option 3: Monthly Interest rate = 6 / 12 = 0.5%
Present Value = 850 x PVAF(0.5%, 84 periods) = 850 x 68.453 = $58,185.09

(b) Since there is a difference of years and difference of payment scheme as well under both the options. It is practically not possible to calculate to calculate the interest rate at which both the options are equal. If there are methods then it cannot be done manually using the pre-defined formulas. But we can get an idea from the above answer that the interest rate would be approximately around 6% only since there is not much difference between the present value under both the options.

Related Questions

Navigate

• Browse (All)
• Browse 3
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.