Use the formula for the present value of an ordinary annuity

Use the formula for the present value of an ordinary annuity or the amortization formula to solve the following problem.

PV=$18,000, i= 0.005, PMT=$300, n= ?

Solution

The formula for the present value of an ordinary annuity is P =p[ (1-(1+i)^-n]/i , where, P is the present value, i is the rate per period (term), p is the payment per period/term (PMT) and n is the number of periods/terms. Here, P = $18000, p = $300 and i = 0.005. Hence, 18000 = 300 [1-(1+0.005)^-n]/0.005 or, [1- (1.0.005)^-n]= 18000*0.005/300 = 0.3 so that (1.0.005)^-n = 1-0.3 = 0.7. Now, on taking logarithm of both the sides, we get –n log1.005 = log 0.7 or, -n*0.002166061757 = -0.15490196. Hence n =0.15490196/ 0.002166061757 = 71.51317801, say 72 ( on rounding off to the nearest whole number). Thus, n =72.