Question

A used piece of rental equipment has 2 1/ 2 years of useful life remaining. When rented, the equipment brings in $700 per month (paid at the beginning of the month). If the equipment is sold now and money is worth 4.3%, compounded monthly, what must the selling price be to recoup the income that the rental company loses by selling the equipment "early"? (a) Decide whether the problem relates to an ordinary annuity or an annuity due. (b) Solve the problem. (Round your answer to the nearest cent.)

Answer 1

(a). The problem relates to an annuity due as the payments are made at the beginning of the month.

(b). The annuity due payment formula is PV = P+(P/r)[1-(1+r)^-(n-1)] where PV is the present value, P is the periodic payment at the beginning of the period , r is the rate per period and n is the number of periods.

Here, P = $ 700, r = 4.3/1200, and n = 2.5*12 = 30.

Therefore, PV = 700+[700/(4.3/1200)]*[ 1-(1+4.3/1200)^-29] = 700+ (700*1200/4.3)* 0.098532173 = 700+ 19248.15 = $ 19948.15 ( on rounding off to the nearest cent).

Thus, the selling price must be $ 19948.15 to recoup the income that the rental company loses by selling the equipment "early".