Question

A debt of $2,000 will be repaid by monthly payments of $600 for as long as necessary, the first payment to be made at the end of 6 months. If interest is at j12 = 9%, find the size of the debt at the end of 5 months and make out the complete amortization schedule starting at that time.

Answer 1

Annual interest rate=9%

Calculation of monthly interest rate:

Let monthly interest rate be x.

so,

(1+x)^{^12}=1.09

1+x=1.09^{^(1/12)}

x=.007207 or .7207% per month.

Size of debt at the end of 5 month=2000*(1.007207)^{^5}

=2073.12

Amortisation schedule:

Rate of interest		0.007207
Month end	Loan Outstanding	Interest	Installment Amount	Principal Repaid	Loan Balance
6	2073.12	14.94098	600	585.0590242	1488.060976
7	1488.060976	10.72446	600	589.2755445	898.7854313
8	898.7854313	6.477547	600	593.5224534	305.2629779
9	305.2629779	2.20003	600	597.7999697	-292.5369918

at the end of 9th month loan becomes negative hence repayment date should be somthing in between 8th and 9th month end. which can be found by using nper function in excel as follows:

Function Arguments NPER Rate 0.007207 Pmt 600 Pv -2073.12 B 6 6 6 = 0.007207 = 600 = -2073.12 = number Fv Type 0 3.511541207 Returns the number of periods for an investment based on periodic, constant payments and a constant interest rate. Rate is the interest rate per period. For example, use 6%/4 for quarterly payments at 6% APR. Formula result = 3.511541207 Help on this function OK Cancel

answer is 3.51 periods means loan repayment shall be done completely after 9.51 months (i.e. 6+3.51)

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