21 Suppose you take out a 48-month installment loan to finance a
piano for $2,330. The...
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21 Suppose you take out a 48-month installment loan to finance apiano for $2,330. The payments are $67.96 per month and the totalfinance charge is $932.08. After 24 months, you decide to pay offthe loan. After calculating the finance charge rebate, find yourloan payoff.
Answer & Explanation
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4.0 Ratings (425 Votes)
Loan payoff is $ 1,366.02
Step-1:Calculation of monthly interest rate
Monthly
interest rate
=
=rate(nper,pmt,pv)
=
1.47%
Where,
nper
48
pmt
$ 67.96
pv
$
-2,330.00
Step-2:Calculation of loan payoff
Loan is the
present value of monthly payment.
Loan amount
after 24 months is the present value of monthly payment of balance
monthly payment.
Loan
payoff
=
Monthly payment
*
Present
value of annuity of 1
=
$ 67.96
*
20.10037
=
$
1,366.02
Working:
Present
value of annuity of 1
=
(1-(1+i)^-n)/i
Where,
=
(1-(1+0.0147)^-24)/0.0147
i
1.47%
=
20.100369
n
24
Total
repayment
=
$
1,366.02
+
$ 67.96
*
24
=
$
2,997.06
Loan
amount
$
2,330.00
Finance
charge actually paid
$ 667.06
Earlier
estimated total finance charge
$ 932.08
Finance
charge rebate
$ 932.08
-
$
667.06
=
$ 265.02
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