Question

The present worth of purchase over 6-year period was $550000. If the costs are known to have increased geometrically by 7% per year during that time and the company uses an interest rate of 13% per year for investments, what was the cost in year 1? (hint: base amount)

Answer 1

Formula :

Present worth(PW) of geometrically increasing periodic payment is given by :

PW = (P/(r - g))(1 - ((1 + g)/(1 + r))ⁿ)

where PW = Present worth = 550,000 , P = Base Payment or Payment(or cost) in year 1 that we have to calculate, r = interest rate = 13% = 0.13, g = growth rate = 7% = 0.07 and n = time period = 6

Thus using above formula and information we get :

550,000 = (P/(0.13 - 0.07))(1 - ((1 + 0.07)/(1 + 0.13))⁶)

=> P = 118206.95 {Base amount}

Hence, the cost in year 1 = $118206.95