Calculate compound interest on 80000 at 13% p.a. for one year if the interest is compounded half yearly. (a) 10400 (b) 10738 (c) 11400 (d) 11700
Answers
Answer:
Economics is a social science concerned with the production, distribution, and consumption of goods and services. It studies how individuals, businesses, governments, and nations make choices about how to allocate resources
Step-by-step explanation:
Here, Principal (P) = Rs. 80000, Time (n) = 1\ \frac{1}{2} years, Rate of interest (R) = 10%
Amount for 1 year (A) = P\left(1+\frac{R}{100}\right)^n
= 80000\left(1+\frac{10}{100}\right)^1
= 80000\left(1+\frac{1}{10}\right)^1
= 80000\left(\frac{11}{10}\right)^1
= Rs. 88,000
Interest for \frac{1}{2} year = \frac{88000\times10\times1}{100\times2}
= Rs. 4,400
Total amount = Rs. 88,000 + Rs. 4,400 = Rs. 92,400
(ii) Here, Principal (P) = Rs. 80,000
Time(n) = 1\ \frac{1}{2} year = 3 years (compounded half yearly)
Rate of interest (R) = 10% = 5% (compounded half yearly)
Amount (A) = P\left(1+\frac{R}{100}\right)^n
= 80000\left(1+\frac{5}{100}\right)^3
= 80000\left(1+\frac{1}{20}\right)^3
= 80000\left(\frac{21}{20}\right)^3
= 80000\times\frac{21}{20}\times\frac{21}{20}\times\frac{21}{20}
= Rs. 92,610
Difference in amounts
= Rs. 92,610 – Rs. 92,400 = Rs. 210