Question

Suppose that a loan is being repaid with 60 equal monthly payments, the first coming a month after the loan is made. If the rate of interest is 9.7 percent convertible monthly, and the amount of principal in the 22nd payment is 260, how much interest is in the 44th payment?

Answer 1

If the loan amount is $100 then the percent of principal paid on 22nd payment is 1.5414%

Principal paid (nth payment)	=	Payment ÷ [1+R)^(N-n+1)
Payment		2.1100
Rate of interest	R=	0.8083%
nth payment	n=	22
Total payments	N=	60
Principal paid	=	2.11/[1+0.008083^(60-22+1)
Principal paid	=	1.5414

Monthly payment	=	[P * R * (1+R)^N ] / [(1+R)^N -1]
Using the formula:
Loan amount	P	100.00
Rate of interest per period:
Annual rate of interest		9.700%
Frequency of payment	=	Once in 1 month period
Numer of payments in a year	=	12/1 =	12
Rate of interest per period	R	0.097 /12 =	0.8083%
Total number of payments:
Frequency of payment	=	Once in 1 month period
Number of years of loan repayment	=	5
Total number of payments	N	5*12 =	60
Period payment using the formula	=	[ 100*0.00808*(1+0.00808)^60] / [(1+0.00808 ^60 -1]
Monthly payment	=	2.1100

As principal paid on 22nd payment is 1.5414%, loan amount is 260/1.5414% = 16,867.76

Now the monthly payment on loan amount is:

Monthly payment	=	[P * R * (1+R)^N ] / [(1+R)^N -1]
Using the formula:
Loan amount	P	16,867.76
Rate of interest per period:
Annual rate of interest		9.700%
Frequency of payment	=	Once in 1 month period
Numer of payments in a year	=	12/1 =	12
Rate of interest per period	R	0.097 /12 =	0.8083%
Total number of payments:
Frequency of payment	=	Once in 1 month period
Number of years of loan repayment	=	5
Total number of payments	N	5*12 =	60
Period payment using the formula	=	[ 16867.76*0.00808*(1+0.00808)^60] / [(1+0.00808 ^60 -1]
Monthly payment	=	355.91

Interest paid on 44th payment is:

Principal paid (nth payment)	=	Payment ÷ [1+R)^(N-n+1)
Payment		355.91
Rate of interest	R=	0.8083%
nth payment	n=	44
Total payments	N=	60
Principal paid	=	355.91/[1+0.008083^(60-44+1)
Principal paid	=	310.38091
Interest paid ( balance)	=	45.52