A loan of 1000 at a nominal rate of 12 percent convertible monthly is to be...

A loan of 1000 at a nominal rate of 12 percent convertible monthly is to be repaid by six monthly payments with the first payment due at the end of 1 month. The first three payments are x each, and the final three payments are 3x each.

Determine the sum of the principal repaid in the third payment and the interest paid in the fifth payment.

Solutions

Expert Solution

Monthly Rate = 0.12/12 = 0.01

Period	Discounting Factor [1/(1.01^period)]
1	0.99009901
2	0.980296049
3	0.970590148
Total	2.940985207
4	0.960980344
5	0.951465688
6	0.942045235
Total	2.854491267

Loan Amount = [First 3 Payments*Total of Discounting Factor of first 3 payments]+[Next 3 Payments*Total of Discounting Factor of next 3 payments]

1000 = 2.940985207x + 2.854491267(3x)

1000 = 2.940985207x + 8.563473801x

1000 = 11.504459008x

Therefore, x = 1000/11.504459008 = $86.92 and 3x = 3*86.92 = $260.76

Amortization Schedule:

Period	Opening Principal (previous closing)	Interest (opening*0.01)	Installment	Principal Repayment (installment-interest)	Closing Principal (opening-principal repayment)
1	1000	10	86.92	76.92	923.08
2	923.08	9.2308	86.92	77.6892	845.3908
3	845.3908	8.453908	86.92	78.466092 = $78.47	766.924708
4	766.924708	7.66924708	260.76	253.0907529	513.8339551
5	513.8339551	5.138339551 = $5.14	260.76	255.6216604	258.2122946
6	258.2122946	2.582122946	260.79442	258.2122946	0

jeff jeffy answered 2 years ago

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