On September 1, 2013, Susan Chao bought a motorcycle for $21,000. She paid $1,100 down and...

On September 1, 2013, Susan Chao bought a motorcycle for $21,000. She paid $1,100 down and financed the balance with a five-year loan at an APR of 6.3 percent, compounded monthly. She started the monthly payments exactly one month after the purchase (i.e., October 1, 2013). Two years later, at the end of October 2015, Susan got a new job and decided to pay off the loan. If the bank charges her a 2 percent prepayment penalty based on the loan balance, how much must she pay the bank on November 1, 2015? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Solutions

Expert Solution

EMI = P*i*(1+i)^n/[{(1+i)^n}-1]

Where,

P = Principal = 21000-1100 = 19900

i= Interest Rate = 0.063/12 = 0.00525

n= Number of periods = 5*12 = 60

Therefore, EMI = 19900*0.00525*(1+0.00525)^60/[{(1+0.00525)^60}-1]

= 104.475*(1.36913)/[1.36913-1] = 143.0399/0.36913 = $387.51

October 1, 2013 to October 1, 2015 are 25 Installments.

Period	Opening Principal (previous closing)	Interest (opening*0.00525)	Installment	Principal Repayment (installment-interest)	Closing Principal (opening-principal repayment)
1	19900	104.475	387.51	283.035	19616.965
2	19616.965	102.9890663	387.51	284.520934	19332.4441
3	19332.4441	101.4953313	387.51	286.014669	19046.4294
4	19046.4294	99.99375434	387.51	287.516246	18758.9132
5	18758.9132	98.48429405	387.51	289.025706	18469.8874
6	18469.8874	96.96690909	387.51	290.543091	18179.3444
7	18179.3444	95.44155786	387.51	292.068442	17887.2759
8	17887.2759	93.90819854	387.51	293.601801	17593.6741
9	17593.6741	92.36678909	387.51	295.143211	17298.5309
10	17298.5309	90.81728723	387.51	296.692713	17001.8382
11	17001.8382	89.25965049	387.51	298.25035	16703.5878
12	16703.5878	87.69383615	387.51	299.816164	16403.7717
13	16403.7717	86.11980129	387.51	301.390199	16102.3815
14	16102.3815	84.53750275	387.51	302.972497	15799.409
15	15799.409	82.94689714	387.51	304.563103	15494.8459
16	15494.8459	81.34794085	387.51	306.162059	15188.6838
17	15188.6838	79.74059004	387.51	307.76941	14880.9144
18	14880.9144	78.12480063	387.51	309.385199	14571.5292
19	14571.5292	76.50052834	387.51	311.009472	14260.5197
20	14260.5197	74.86772861	387.51	312.642271	13947.8775
21	13947.8775	73.22635669	387.51	314.283643	13633.5938
22	13633.5938	71.57636756	387.51	315.933632	13317.6602
23	13317.6602	69.91771599	387.51	317.592284	13000.0679
24	13000.0679	68.2503565	387.51	319.259644	12680.8083
25	12680.8083	66.57424337	387.51	320.935757	12359.8725
26	12359.8725	64.88933065	0	-64.8893306	12424.7618

Upto 25th Installment i.e. Upto October 1, 2015, Regular Installment will be paid. But, on 26th Installmet i.e. November 1, 2015, It will Not be paid.

Balance as on November 1, 2015 = $12424.76

Amount Payable to Pay Off the Loan = Balance as on November 1, 2015 + Penalty = 12424.76+2% = $12673.26

Amount to be paid

jeff jeffy answered 1 year ago

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