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

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?

• You have missing brackets. Should be `L = (B + (M ((1 + R)^N - 1)/R))/(1 + R)^N`. – Chris Degnen Feb 12 '17 at 15:05

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

``````B = p * L
``````

``````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)
``````

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
``````