LOAN payment with 15% p.a. interest $_$
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LOAN payment with 15% p.a. interest $_$

[From: ] [author: ] [Date: 11-12-27] [Hit: ]
is paid back in 5 annual instalments.a) what is the amount of each instalment?b) how much is paid back altogether?the answer for a) $1835.68 and b) $9178.thank youin advance-since the interest is charged monthly,......
A loan of $6000 over 5 years at 15% p.a. interest, charged monthly, is paid back in 5 annual instalments.

a) what is the amount of each instalment?
b) how much is paid back altogether?

the answer for a) $1835.68 and b) $9178.41

please show DETAILED work out
thank you in advance

-
since the interest is charged monthly,
interest/yr on $100 will be 100(1+0.15/12)^12 - 100 ≈ 16.07545%
PV = present value of loan
PMT = periodic payments
r = effective interest rate, decimals
n = period of payments

the formula is
PMT = PVr / (1 - (1+r)^-n)
= 6000*0.1607545 /(1 - 1.1607545^-5)
= $1835.68252 = $1835.68 <------

total payments = 5*1835.68252 = $9178.41 <--------
[ normally it is calculated as 5*1835.68 = $9178.40 ]

-
Annual amortization:
= 6,000.00(Annuity of 5 years of 1, interest annually ([1 + 15%/12]¹² - 1) OR 16.07545177%
= 6,000.00(0.30594709897)
= 1,835.68

Total pay back in 5 years:
= 5(1,835.68)
= 9,178.40

Answer: a) $1,835.68; b) $9,178.40
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