Question

simple and compound interest 10c exercise​

Answer 1

• ᴀɴꜱᴡᴇʀ :

ꜱɪᴍᴘʟᴇ ɪɴᴛᴇʀᴇꜱᴛ ɪꜱ ᴄᴀʟᴄᴜʟᴀᴛᴇᴅ ᴏɴ ᴛʜᴇ ᴘʀɪɴᴄɪᴘᴀʟ, ᴏʀ ᴏʀɪɢɪɴᴀʟ, ᴀᴍᴏᴜɴᴛ ᴏꜰ ᴀ ʟᴏᴀɴ. ᴄᴏᴍᴘᴏᴜɴᴅ ɪɴᴛᴇʀᴇꜱᴛ ɪꜱ ᴄᴀʟᴄᴜʟᴀᴛᴇᴅ ᴏɴ ᴛʜᴇ ᴘʀɪɴᴄɪᴘᴀʟ ᴀᴍᴏᴜɴᴛ ᴀɴᴅ ᴀʟꜱᴏ ᴏɴ ᴛʜᴇ ᴀᴄᴄᴜᴍᴜʟᴀᴛᴇᴅ ɪɴᴛᴇʀᴇꜱᴛ ᴏꜰ ᴘʀᴇᴠɪᴏᴜꜱ ᴘᴇʀɪᴏᴅꜱ, ᴀɴᴅ ᴄᴀɴ ᴛʜᴜꜱ ʙᴇ ʀᴇɢᴀʀᴅᴇᴅ ᴀꜱ "ɪɴᴛᴇʀᴇꜱᴛ ᴏɴ ɪɴᴛᴇʀᴇꜱᴛ

• ꜱᴛᴇᴘ ʙʏ ꜱᴛᴇᴘ ᴇxᴘʟᴀɴᴀᴛɪᴏɴ :

• ᴅɪꜰꜰᴇʀᴇɴᴄᴇ ʙᴇᴛᴡᴇᴇɴ ꜱɪᴍᴘʟᴇ ɪɴᴛᴇʀᴇꜱᴛ ᴀɴᴅ ᴄᴏᴍᴘᴏᴜɴᴅ ɪɴᴛᴇʀᴇꜱᴛ :

ᴛʜᴇ ᴍᴀᴊᴏʀ ᴅɪꜰꜰᴇʀᴇɴᴄᴇ ʙᴇᴛᴡᴇᴇɴ ꜱɪᴍᴘʟᴇ ɪɴᴛᴇʀᴇꜱᴛ ᴀɴᴅ ᴄᴏᴍᴘᴏᴜɴᴅ ɪɴᴛᴇʀᴇꜱᴛ ɪꜱ ᴛʜᴀᴛ ꜱɪᴍᴘʟᴇ ɪɴᴛᴇʀᴇꜱᴛ ɪꜱ ʙᴀꜱᴇᴅ ᴏɴ ᴘʀɪɴᴄɪᴘᴀʟ ᴀᴍᴏᴜɴᴛ ᴡʜᴇʀᴇᴀꜱ ᴄᴏᴍᴘᴏᴜɴᴅ ɪɴᴛᴇʀᴇꜱᴛ ɪꜱ ʙᴀꜱᴇᴅ ᴏɴ ᴛʜᴇ ᴘʀɪɴᴄɪᴘᴀʟ ᴀᴍᴏᴜɴᴛ ᴀɴᴅ ᴛʜᴇ ɪɴᴛᴇʀᴇꜱᴛ ᴄᴏᴍᴘᴏᴜɴᴅᴇᴅ ꜰᴏʀ ᴀ ᴄʏᴄʟᴇ ᴏꜰ ᴛʜᴇ ᴘᴇʀɪᴏᴅ.

ᴡᴇ ᴋɴᴏᴡ ᴛʜᴀᴛ ꜱɪᴍᴘʟᴇ ɪɴᴛᴇʀᴇꜱᴛ ᴀɴᴅ ᴛʜᴇ ᴄᴏᴍᴘᴏᴜɴᴅ ɪɴᴛᴇʀᴇꜱᴛ ᴀʀᴇ ᴛʜᴇ ᴛᴡᴏ ɪᴍᴘᴏʀᴛᴀɴᴛ ᴄᴏɴᴄᴇᴘᴛꜱ ᴡɪᴅᴇʟʏ ᴜꜱᴇᴅ ɪɴ ᴍᴀɴʏ ꜰɪɴᴀɴᴄɪᴀʟ ꜱᴇʀᴠɪᴄᴇꜱ ᴍᴏꜱᴛ ᴇꜱᴘᴇᴄɪᴀʟʟʏ ɪɴ ʙᴀɴᴋɪɴɢ ᴘᴜʀᴘᴏꜱᴇꜱ. ʟᴏᴀɴꜱ ꜱᴜᴄʜ ᴀꜱ ɪɴꜱᴛᴀʟᴍᴇɴᴛꜱ ʟᴏᴀɴꜱ, ᴀᴜᴛᴏ ʟᴏᴀɴꜱ, ᴇᴅᴜᴄᴀᴛɪᴏɴᴀʟ ʟᴏᴀɴꜱ, ᴍᴏʀᴛɢᴀɢᴇꜱ ᴜꜱᴇ ꜱɪᴍᴘʟᴇ ɪɴᴛᴇʀᴇꜱᴛ. ᴛʜᴇ ᴄᴏᴍᴘᴏᴜɴᴅ ɪɴᴛᴇʀᴇꜱᴛ ɪꜱ ᴜꜱᴇᴅ ʙʏ ᴍᴏꜱᴛ ᴏꜰ ᴛʜᴇ ꜱᴀᴠɪɴɢꜱ ᴀᴄᴄᴏᴜɴᴛ ᴀꜱ ɪᴛ ᴘᴀʏꜱ ᴛʜᴇ ɪɴᴛᴇʀᴇꜱᴛ. ɪᴛ ᴘᴀʏꜱ ᴍᴏʀᴇ ᴛʜᴀɴ ᴛʜᴇ ꜱɪᴍᴘʟᴇ ɪɴᴛᴇʀᴇꜱᴛ. ɪɴ ᴛʜɪꜱ ᴀʀᴛɪᴄʟᴇ, ʟᴇᴛ ᴜꜱ ᴅɪꜱᴄᴜꜱꜱ ᴛʜᴇ ᴅɪꜰꜰᴇʀᴇɴᴄᴇ ʙᴇᴛᴡᴇᴇɴ ᴛʜᴇ ꜱɪᴍᴘʟᴇ ɪɴᴛᴇʀᴇꜱᴛ ᴀɴᴅ ᴛʜᴇ ᴄᴏᴍᴘᴏᴜɴᴅ ɪɴᴛᴇʀᴇꜱᴛ ɪɴ ᴅᴇᴛᴀɪʟ.

• ᴅᴇꜰɪɴɪᴛɪᴏɴ ᴏꜰ ꜱɪᴍᴘʟᴇ ᴀɴᴅ ᴄᴏᴍᴘᴏᴜɴᴅ ɪɴᴛᴇʀᴇꜱᴛ :

• ꜱɪᴍᴘʟᴇ ɪɴᴛᴇʀᴇꜱᴛ:

ᴛʜᴇ ꜱɪᴍᴘʟᴇ ɪɴᴛᴇʀᴇꜱᴛ ᴄᴀɴ ʙᴇ ᴅᴇꜰɪɴᴇᴅ ᴀꜱ ᴛʜᴇ ᴘʀɪɴᴄɪᴘᴀʟ ᴀᴍᴏᴜɴᴛ ᴏꜰ ʟᴏᴀɴ ᴏʀ ᴅᴇᴘᴏꜱɪᴛ, ᴀ ᴘᴇʀꜱᴏɴ ᴍᴀᴋᴇꜱ ɪɴᴛᴏ ᴛʜᴇɪʀ ʙᴀɴᴋ ᴀᴄᴄᴏᴜɴᴛ.

• ᴄᴏᴍᴘᴏᴜɴᴅ ɪɴᴛᴇʀᴇꜱᴛ:

ᴛʜᴇ ᴄᴏᴍᴘᴏᴜɴᴅ ɪɴᴛᴇʀᴇꜱᴛ ɪꜱ ꜱɪᴍᴘʟʏ ᴛʜᴇ ɪɴᴛᴇʀᴇꜱᴛ ᴛʜᴀᴛ ᴀᴄᴄᴜᴍᴜʟᴀᴛᴇꜱ ᴀɴᴅ ᴄᴏᴍᴘᴏᴜɴᴅꜱ ᴏᴠᴇʀ ᴛʜᴇ ᴘʀɪɴᴄɪᴘᴀʟ ᴀᴍᴏᴜɴᴛ.

• ᴡʜᴀᴛ ɪꜱ ᴛʜᴇ ꜰᴏʀᴍᴜʟᴀ ꜰᴏʀ ꜱɪᴍᴘʟᴇ ɪɴᴛᴇʀᴇꜱᴛ?

ᴛʜᴇ ꜰᴏʀᴍᴜʟᴀ ꜰᴏʀ ꜱɪᴍᴘʟᴇ ɪɴᴛᴇʀᴇꜱᴛ ɪꜱ ɢɪᴠᴇɴ ʙʏ:

ꜱɪ = (ᴘxʀxᴛ)/100

ᴡʜᴇʀᴇ ꜱɪ = ꜱɪᴍᴘʟᴇ ɪɴᴛᴇʀᴇꜱᴛ

ᴘ = ᴘʀɪɴᴄɪᴘᴀʟ ᴀᴍᴏᴜɴᴛ

ʀ = ʀᴀᴛᴇ ᴏꜰ ɪɴᴛᴇʀᴇꜱᴛ

ᴛ = ᴛɪᴍᴇ ᴅᴜʀᴀᴛɪᴏɴ ɪɴ ʏᴇᴀʀꜱ

• ᴡʜᴀᴛ ɪꜱ ᴛʜᴇ ꜰᴏʀᴍᴜʟᴀ ꜰᴏʀ ᴄᴏᴍᴘᴏᴜɴᴅ ɪɴᴛᴇʀᴇꜱᴛ?

ᴛʜᴇ ꜰᴏʀᴍᴜʟᴀ ꜰᴏʀ ᴄᴏᴍᴘᴏᴜɴᴅ ɪɴᴛᴇʀᴇꜱᴛ ɪꜱ ɢɪᴠᴇɴ ʙʏ:

ᴄɪ = ᴀᴍᴏᴜɴᴛ – ᴘʀɪɴᴄɪᴘᴀʟ

ᴀɴᴅ ᴀᴍᴏᴜɴᴛ = ᴘ(1+ʀ/ɴ)ɴᴛ