Question

John takes a $3000 loan from a bank at an annual effective interest rate of %15. She plans to pay off her debt with 35 monthly payments of $100 and a final balloon payment at the end of 3rd year. Find the value of balloon payment

Answer 1

Sol

Loan amount = $3000

Effective annual rate (r) = 15% p.a, Monthly rate = 15%/12 = 1.25%

Period (n) = 35 months

Monthly payment = $100

We have to compute the present value of annuity factor (PVIFA) from the following equation:

PVIFA = (1 - (1 + r)^-n) / r

PVIFA = (1 - (1 + 1.25%)^-35) / 1.25%

PVIFA = (1 - (1.0125)^-35) / 0.125

PVIFA = 28.207858

Now we have to compute the present value (PV) of monthly payments, from the following equation:

PV = Monthly payment x PVIFA

PV = 100 x 28.207858 = $2820.7858

Now compute the value of balloon payment from the following equation:

Balloon payment = Loan amount - PV of monthly payments x (1 + r)^n

Balloon payment = (3000 - 2820.7858) x (1 + 1.25%)^35

Balloon payment = 179.21 x (1.0125)^35 = $276.82

Therefore value of balloon payment will be $276.82