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Today's Question ✌
Q.Calculate the compound interest for the second year on ₹8000 invested for 3 yrs at 10%p.a.
Also find the sum due at the end of third year.
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Answers
cosA=5/13
sinA=-√(1-cos^2A) (since theta is in 4th quadrant)
i.e. sinA=-√144/169
=-12/13
tanB=-15/8
sinB=+(15)/√{(-15)^2+(8)^2} (B is in Q2)
i.e. sinB=15/17
cosB=tanB/sinB
i.e. cosB=-15/8 * 17/15
cosB=17/8
now
sin(A+B)=sinAcosB+cosAsinB
sin(A+B)=(-12/13)(17/8)+(5/13)(15/17)
={1/13}(-51/2 + 75/17)
=(1/13)(-710/34)
=-710/442
Answer:-
ʟᴇᴛ ᴍᴇ ɪɴᴛʀᴏᴅᴜᴄᴇ ᴛʜᴇ ʀᴇᴀᴅᴇʀ ᴛᴏ ᴛʜᴇ ᴄᴏɴᴄᴇᴘᴛ ᴏғ ᴇғғᴇᴄᴛɪᴠᴇ ʀᴀᴛᴇ ᴏғ ɪɴᴛᴇʀᴇsᴛ.
ʟᴇᴛ ᴜs ᴛᴀᴋᴇ ᴀ sɪᴍᴘʟᴇʀ ᴄᴀsᴇ ᴏғ 5% ɪɴᴛᴇʀᴇsᴛ ғᴏʀ ᴛᴡᴏ ʏᴇᴀʀs.
ɪɴ ᴛᴡᴏ ʏᴇᴀʀs, sɪ ᴡɪʟʟ ʙᴇ 10%
ᴡʜᴀᴛ ʜᴀᴘᴘᴇɴs ᴛᴏ ᴄɪ ᴀғᴛᴇʀ ᴛᴡᴏ ʏᴇᴀʀs ?
ɪᴛ ɪs 5% + (5% + 5% ᴏɴ 5%) = 10.25%
ᴛʜᴇsᴇ ᴛᴡᴏ % ғɪɢᴜʀᴇs ᴀʀᴇ ᴇғғᴇᴄᴛɪᴠᴇ ʀᴀᴛᴇs ᴏғ ɪɴᴛᴇʀᴇsᴛ.
sɪᴍɪʟᴀʀʟʏ, ɪɴ ᴛʜʀᴇᴇ ʏᴇᴀʀs, sɪ ɪs 15% ᴀɴᴅ ᴄɪ ᴡɪʟʟ ʙᴇ 15.7625%
ᴛʜᴇ ᴅɪғғᴇʀᴇɴᴄᴇ ʙᴇᴛᴡᴇᴇɴ ᴛʜᴇsᴇ ᴛᴡᴏ ɪs (15.7625 - 15)% = 0.7625%
ɴᴏᴡ, 15.25 ɪs 0.7625% ᴏғ ᴡʜᴀᴛ ?
0.7625% x ᴘ = 15.25
=> ᴘ = 2000
ɴᴏᴡ, ᴛʜᴇʀᴇ ɪs ᴀɴ ᴇғғɪᴄɪᴇɴᴛ ᴍᴇᴛʜᴏᴅ ᴛᴏ ᴅᴇᴛᴇʀᴍɪɴᴇ ᴇғғᴇᴄᴛɪᴠᴇ ʀᴀᴛᴇ ᴏғ ɪɴᴛᴇʀᴇsᴛ ɪɴ ᴄᴀsᴇ ᴏғ ᴄɪ ᴛʜᴀᴛ ᴡᴏᴜʟᴅ ʙᴇ ᴏғ ᴘᴀʀᴛɪᴄᴜʟᴀʀ ɪɴᴛᴇʀᴇsᴛ ᴛᴏ ᴄᴏᴍᴘᴇᴛɪᴛɪᴠᴇ / ᴀᴘᴛɪᴛᴜᴅᴇ ᴛᴇsᴛ ᴛᴀᴋᴇʀs.
ᴀɴᴅ ᴛʜᴀᴛ ɪs :
ᴀ + ʙ + ᴀʙ/100
ғᴏʀ ᴛᴡᴏ ʏᴇᴀʀs, ᴊᴜsᴛ ᴘʟᴜɢ ɪɴ ᴛʜᴇ ᴠᴀʟᴜᴇs ᴏғ ᴀ & ʙ ᴀs 5% ᴀɴᴅ ɢᴇᴛ ɪɴsᴛᴀɴᴛ ʀᴇsᴜʟᴛ ᴏғ :
5 + 5 + (5 x 5)/100 = 10.25%
ғᴏʀ ᴛʜʀᴇᴇ ʏᴇᴀʀs, ᴘʟᴜɢ ɪɴ ᴠᴀʟᴜᴇs ᴏғ ᴀ & ʙ ᴀs 10.25% ᴀɴᴅ 5% ʀᴇsᴘᴇᴄᴛɪᴠᴇʟʏ ᴀɴᴅ ɢᴇᴛ ғɪɴᴀʟ ʀᴇsᴜʟᴛ :
10.25 + 5 + (10.25 x 5)/100 = 15.7625%
ᴛʜɪs ᴘʀᴏᴄᴇss ᴄᴀɴ ʙᴇ ᴇxᴛᴇɴᴅᴇᴅ ᴛᴏ ᴀɴʏ ɴᴜᴍʙᴇʀ ᴏғ ʏᴇᴀʀs.