Question

The present worth of purchase over 6-year period was $350000. 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)

Select one:

a. 118207

b. 56281

c. 215621

d. 193430

e. 75223

Answer 1

The correct answer is (e) 75223

Formula for Present worth(PW) of geometrically growing annuity or periodic payment is:

where PW = Present worth = 350,000 , P = First period cost or cost in period 1 that we have to calculate, r = interest rate = 13% = 13/100 = 0.13, g = growth rate = 7% = 7/100 = 0.07 and t = number of time period or number of years as here 1 period is 1 year and so, t = 6

Thus using information from the question and above formula we have :

=> P = 350,000/4.65285679 = 75223(approx)

Therefore, cost in period 1 or First period cost = $75223

Hence, the correct answer is (e) 75223