Question

Theory of Interest: Sally takes out a $7,000 loan which requires 60 equal monthly payments starting at the end of the first month. The nominal annual interest rate is 8% convertible monthly. She arranges to make no payments for the first five months and then make the same payments she would have made plus an extra payment at the end of the 60th month. How much will this balloon payment be? Answer: $1,178.41. If you are using Excel worksheets, please tell what formulas are you using to solve the problem.

Answer 1

EMI = [P x R x (1+R)^N]/[(1+R)^N-1]
Where,
EMI= Equal Monthly Payment
P= Loan Amount
R= Interest rate per period (8%/12)
N= Number of periods
= [ $7000x0.007 x (1+0.007)^60]/[(1+0.0067)^60 -1]
= [ $46.66662( 1.007 )^60] / [(1.007 )^60 -1
=$141.9347
The monthly payment would be = $141.9347
The first five month payment have been deferred till 60th payment hence we need to calculate
future value of fisrt five months payment
Month	Calculation	Future Value
1	=$141.9347*(1.00667)^59	$          210.10
2	=$141.9347*(1.00667)^58	$          208.71
3	=$141.9347*(1.00667)^57	$          207.33
4	=$141.9347*(1.00667)^56	$          205.95
5	=$141.9347*(1.00667)^555	$          204.59
	Total	$      1,036.68
Ballon of payment = Deferred payment + 60th month's payment
=$1036.68+141.93
=$1178.41
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