Answer to Question #275721 in Financial Math for Rohosafi

Question #275721

A house which is valued at ksh2600,000 appreciated at rate of 12% per year.



I. What will be its value after two and half years?



Ii. After how long will its value be ksh 4200,000





1
Expert's answer
2021-12-06T12:33:12-0500

I. Value of house after two and half years

FV=PV(1+r)nFV=PV(1+r)^{n}


FV=2600000×(1+0.12)2.5FV=2600000\times(1+0.12)^{2.5}

FV=3,451,583.66FV=3,451,583.66


Ii. Time period to reach 4200,000

FV=PV(1+r)nFV=PV(1+r)^{n}


4200000=2600000×(1+0.12)n4200000=2600000\times(1+0.12)^{n}


(1+0.12)n=4200,0002600,000(1+0.12)^{n}=\frac{4200,000}{2600,000}


(1.12)n=1.62(1.12)^{n}=1.62


n×log(1.12)=log(1.62)n\times log(1.12)=log(1.62)


n=log(1.62)log(1.12)n=\frac{log(1.62)}{log(1.12)}


n=0.20950.0492=4.26n=\frac{0.2095}{0.0492}=4.26


This means the value of house will be ksh 4200,000 after 4.26 years.






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