: Algorithm to calculate the Interest on Loan with a Balloon Payment I am trying to understand the algorithm used by My Calculators.com - Balloon Payment Calculator If I enter the following details: Loan amount: 4556.75 Number

Vote Up Vote Down   0 Reactions

Login to give Reaction!

The website uses the same method as described here.

The value of the loan is equal to the sum of the discounted values of the repayments.

? b = ((1 + r) (m + (1 + r)^n (r s - m)))/r

and m = (r ((1 + r)^(1 + n) s - b))/((1 + r) ((1 + r)^n - 1))

where

s = present value of loan
m = periodic repayment
r = periodic rate
b = balloon payment
n = number of periods

Using your figures to calculate the monthly payment.

s = 4556.75
r = 5.75/100/12
b = 3990.37
n = 5

m = (r ((1 + r)^(1 + n) s - b))/((1 + r) ((1 + r)^n - 1)) = 137.78

Note, on the website the a figure of 137.80 is required to arrive at a balloon payment of 3990.37. The interest rounds to 122.62 either way, as shown below.

Using the formula for interest paid to-date derived here.

number of months, x = 6
total interest = ((1 + r)^x - 1) s + (m (1 - (1 + r)^x + r x))/r = 122.62

Website screenshots