Question

(iii) A man borrows 8000 and
agrees repay
with
a total interest of € 1360 in 12 monthly instalments.
Each instalment being less than the preceding one
by 40. Find the amount of the first and last
instalment.

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Answer 1

ᴍᴏɴᴇʏ ʜᴇ ʙᴏʀʀᴏᴡs = 8000

ɪɴᴛᴇʀᴇsᴛ ʜᴇ ᴡɪʟʟ ᴘᴀʏ = 1360

ᴛᴏᴛᴀʟ ᴍᴏɴᴇʏ ʜᴇ ᴡɪʟʟ ᴘᴀʏ ᴀғᴛᴇʀ = 8000 + 1360 = 9360

ɴᴏᴡ ʜᴇ ᴡɪʟʟ ᴘᴀʏ ɪɴ 12 ɪɴsᴛᴀʟʟᴍᴇɴᴛs ᴡɪᴛʜ ᴀ ᴅɪғғᴇʀᴇɴᴄᴇ ᴏғ 40 ɪɴ ᴇᴀᴄʜ ɪɴsᴛᴀʟʟᴍᴇɴᴛ.

ᴛʜɪs ɪs ᴀ ғᴏʀᴍ ᴏғ ᴀᴘ,

ᴡʜᴇʀᴇ ᴄᴏᴍᴍᴏɴ ᴅɪғғᴇʀᴇɴᴄᴇ ᴅ = -40, ɴᴜᴍʙᴇʀ ᴏғ ᴛᴇʀᴍs ɴ = 12, ᴀɴᴅ sᴜᴍ ᴏғ 12 ᴛᴇʀᴍs ɪs 9360

sᴏ,

sᴜᴍ ᴏғ ɴ ᴛᴇʀᴍs ɪɴ ᴀᴘ ɪs

sᴜᴍ = ɴ/2 [ 2ᴀ + (ɴ - 1)ᴅ ]

9360 = 12/2 [ 2ᴀ - 40(12 - 1) ]

9360 = 6 [ 2ᴀ - 440 ]

1560 = 2ᴀ - 440

2ᴀ = 2000

ᴀ = 1000

ɴᴛʜ ᴛᴇʀᴍ ɪɴ ᴀᴘ ɪs ɢɪᴠᴇɴ ʙʏ:

ᴀ(ɴ) = ᴀ + (ɴ - 1)ᴅ

ʟᴀsᴛ ᴛᴇʀᴍ = 1000 - 40(12 - 1)

=1000 - 440 = 560

ᴛʜᴇʀᴇғᴏʀᴇ ғɪʀsᴛ ɪɴsᴛᴀʟʟᴍᴇɴᴛ ɪs 1000 ᴀɴᴅ ʟᴀsᴛ ᴏɴᴇ ɪs 560.