Find the amount that David would receive if he invests Rs. 8192 for 18

1.	Find the amount that David would receive if he invests Rs. 8192 for 18 months at 12% per annum, the interest being compounded half-yearly.
Answer» Given, Principal = Rs.8192 Rate = 12% p.a =\(\frac{12}{2}\)= 6% half yearly Time = 18 months \(=\frac{18}{12}\)\(={1}\frac{1}{2}\) years = 3 half years Hence, Amount \(={P}[({1}+\frac{R}{100})^{time}]\) \(={8192}[({1}+\frac{6}{100})^3]\) \(={8192}\times(\frac{53}{50})^3\) \(={8192}\times\frac{53}{50}\times\frac{53}{50}\times\frac{53}{50}\)= Rs.9826 So, David receives Rs.9826 after 18 months

Find the amount that David would receive if he invests Rs. 8192 for 18 months at 12% per annum, the interest being compounded half-yearly.

Answer»

Given,

Principal = Rs.8192

Rate = 12% p.a =\(\frac{12}{2}\)= 6% half yearly

Time = 18 months \(=\frac{18}{12}\)\(={1}\frac{1}{2}\) years = 3 half years

Hence,

Amount \(={P}[({1}+\frac{R}{100})^{time}]\)

\(={8192}[({1}+\frac{6}{100})^3]\)

\(={8192}\times(\frac{53}{50})^3\)

\(={8192}\times\frac{53}{50}\times\frac{53}{50}\times\frac{53}{50}\)= Rs.9826

So,

David receives Rs.9826 after 18 months