Question

An loan is paid in 3 years with monthly payment starting one month after the loan is made. The payments are 540 each in the first year, and 900 per month in the second year, and 700 each in the last year. Interest is at a nominal rate of 7.8 percent convertible monthly. What is the outstanding balance after the 15th payment. Keep 4 decimal places only.

Answer 1

Loan term = 3 years = 18 months

Payments in first year = 540 per month

Payments in second year = 900 per month

Payments in last/third year = 700 per month

Rate of interest (ROI) = 7.8% convertible monthly

We need to calculate outstanding balance after 15th payment is paid

As the principal amount of loan is not given we need to do reverse calculations as follows :-

Nth month payments	outstanding amount (A)	roi (%)	interest amount (A×7.8%) = (B)	total outstanding amount (A+B) = (C)	installment paid (D)	Net outstanding amount after respective monthly payment (A-D) = (E)
18th month	649 (note 1)	7.8	51	700	700	0
17th month	1251 (note 2)	7.8	98	1349	700	649
16th month	1810 (note 3)	7.8	141	1951	700	1251
15th month	2328 (note 4)	7.8	182	2510	700	1810

Note 1 = let X be the outstanding amount for 18th month then X+ (X ×7.8%) = 700

= X +0.078X = 700

= 1.078X = 700

= X = 700 ÷ 1.078

= X = 649

The outstanding amount for 18th month beginning and 17th month ending = 649

Note 2 :-

Let X be the outstanding amount for the 17th month then X + (X × 7.8%) = 700 + 649 = 1349

= 1.078X = 1349

= X = 1349÷1.078

= X = 1251

The outstanding amount for 17th month beginning and 18th month ending = 1251

Note 3 :-

Same as above 1.078X = 700 + 1251 = 1951

= 1.078X = 1951

= X = 1951 ÷ 1.078

= X = 1810

The outstanding amount for 16th month beginning and 15th month ending is 1810

Note 4 :- same as above 1.078X = 1810+700

= 1.078X = 2510

X = 2510 ÷ 1.078

X = 2328

Then the answer we need is outstanding amount after payment of 15th month payments is 1810

The answer is 1810.

These are all the information required to solve the above given question.

If there is any clarifications required regarding the above provided answer, please mention them in comment box.

I hope, all the above provided information and calculations are useful and helpful to you.

Thank you.