Calculate the Loan Amount for a given Monthly Payment where the Balloon Payment is a Percentage of the Loan Amount

Question

I'm trying to calculate how much you can borrow for a given monthly payment, including a balloon payment, where the balloon payment is given as a percentage of the final loan amount.

The calculation I have for a set balloon amount (rather than percentage) is:

L = Loan Amount, B = Balloon Payment, M = Monthly Payment, R = Monthly Interest, N = Number of Monthly Payments

L = (B + M x ((1 + R)^N - 1 / R)) / (1 + R)^N

How can I calculate the Loan Amount if the Balloon payment is given as a percentage of the loan?

Answer 1

Assuming the percentage is represented as p, we'd have

B = p * L

Copying your original formula:

L = (B + M * ((1 + R)^N - 1 / R)) / (1 + R)^N

Multiplying by (1 + R)^N and substituting for B.

L * (1 + R)^N = p * L + M * ((1 + R)^N - 1 / R)

Subtracting p * L from both sides.

L * (1 + R)^N - p * L = M * ((1 + R)^N - 1 / R)

Combining terms and pulling out the L on the left.

L * ((1 + R)^N - p) = M * ((1 + R)^N - 1 / R)

Isolating L on the left.

L = (M * ((1 + R)^N - 1 / R)) / ((1 + R)^N - p)

Answer 2

The present value of a balloon loan can be expressed as

which can be rewritten as L = (B + (M ((1 + R)^N - 1)/R))/(1 + R)^N

where

L = present value of loan
M = periodic repayment
R = periodic rate
B = balloon payment
N = number of periods

If the balloon B is set as A percent of the loan amount L then B = A L.

∴ L = A L (1 + R)^-N + (M (1 + R)^-N (-1 + (1 + R)^N))/R

∴ L = (M (-1 + (1 + R)^N))/(R (-A + (1 + R)^N))

Example

A = 60% = 0.6
R = 5% = 0.05 per month
M = 10 per month
N = 4 months

∴ L = 70.0257

and balloon payment B = A L = 42.0154

Check

(B + (M ((1 + R)^N - 1)/R))/(1 + R)^N = 70.0257 = L