Mwenga bought a plot of land at sh 300000 per hectare in a town where land value appreciates at a constant rate of 10% per annum. After two years he sold the whole plot to a customer who was willing to pay sh 500000 per hectare. In the transaction Mwenga received sh 274000 more than the present value of the plot. Determine the present land value per hectare. (4 marks)

Solution

Mw e n g a b o ug h t a pl o t o f l an d a t s h 300000 p er h ec t a re in a t o w n w h ere l an d v a l u e a pp rec ia t es a t a co n s t an t r a t e o f 10% p er ann u m . A f t er tw o ye a rs h e so l d t h e w h o l e pl o t t o a c u s t o m er w h o w a s w i ll in g t o p a y s h 500000 p er h ec t a re . I n t h e t r an s a c t i o n Mw e n g a rece i v e d s h 274000 m ore t han t h e p rese n t v a l u e o f t h e pl o t . De t er min e t h e p rese n t l an d v a l u e p er h ec t a re . (4 ma r k s)

Amount : 360000

Solution steps

Translate the problem into an equation:

A = 300000 (1 + 0.1 \cdot 2)

300000 (1 + 0.1 \cdot 2) = 360000

Amount : 360000