Simple & Compound Interest

Concepts:
Simple Interest, SI = PNR/100
Where P is Principal, R is rate of interest and N is the time period in years.Let P is Principal, R is rate of interest and N is time period in years,
When interest is compounded annually,
Amount = P (1+(R/100))^NWhen interest is compounded half yearly,
Amount = P (1+(R/2)/100)^2NWhen interest is compounded quarterly,
Amount = P (1+(R/4)/100) ^4NWhen interest is compounded annually, but time period in fraction say a b/c years
Amount = P*(1+R/100)^a * (1+bR/100c)When rates are different for different years say R1 % , R2 % and R3 % for 1st,2nd and 3rd year respectively
Amount = P (1+ (R1/100)) *(1+ (R2/100)) * (1+ (R3/100))Questions:
Simple interest on a certain sum of money for 3 years at 8% per annum is half the compound interest on Rs. 4000 for 2 years at 10% per annum. Find the sum placed on simple interest.
Let Principal is P
P * 3 * 8/100 = 1/2(4000(110/100)^24000)
6P/25 = 1/2(40 * 121 4000) = 1/2(48404000) = 1/2 (840) = 420
P = 25 * 420/6 = 25 * 70 = 1750Find the difference between simple interest and compound on Rs. 1200 for one year at 10% per annum reckoned halfyearly?
P = 1200 N = 1 YEAR R= 10%
SI = 1200 * 1 * 10/100 = 120 RS
CI = 1200(1+(10/2)/100)^2 – 1200
= 1200 * 441/400 1200
= 1200 * (441/400 – 1)
= 1200 * 41/400
= 123 RS
Difference = 3RSThe difference between compound interest and simple interest on an amount of Rs. 15,000 for 2 years is Rs. 96. What is the rate of interest per annum?
(15000(1+R/100) ^215000) – 15000 * 2 * R/100 = 96
15000((1+R/100) ^21 2R/100) = 96
15000(1+2R/100+R^2/1000012R/100) = 96
15000 * R^2/10000 = 96
3R^2 = 192
R^2 = 64
R = 8%The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is Re. 1. Find the sum.
Let P = 1 Rs
SI = 1 * 2 * 4/100 = 2/25
CI = 1 * (104/100)^2 – 1 = 676/6251 = 51/625
CISI = 51/625 – 2/25
= 5150/625 = 1/625
Hence for 1 Rs sum difference is 1/625 Rs
So for getting 1 Rs difference Sum will be 625 Rs.The compound interest on Rs. 30,000 at 7% per annum is Rs. 4347. Find the period (in years)
Total Amount = 30000+4347 = 34347
34347 = 30000 * (1+7/100) ^N
(107/100)^N = 34347/30000 = 11449/10000
(107/100)^N = 11449/10000
N = 2 Years