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21 Suppose you take out a 48-month installment loan to finance a piano for $2,330. The...

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Finance

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.

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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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