Question

Amanda Rice has just arranged to purchase a $500,000 vacation home in the Bahamas with a 20 percent down payment. The mortgage has a 5.6 percent APR compounded monthly and calls for equal monthly payments over the next 30 years. Her first payment will be due one month from now. However, the mortgage has an eight-year balloon payment, meaning that the balance of the loan must be paid off at the end of Year 8. There were no other transaction costs or finance charges. How much will Amanda’s balloon payment be in eight years? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

ballon payment: $ 435,151.67

Step-by-step explanation:

We need to solve for the PMT fo the mortgage

Then, the amount amortized for the mortage over an 8 years period

Last, we subtract the amortized amount on the principal to knwo the balloon payment.

`PV / (1-(1+r)^(-time) )/(rate) = C\\`

PV 500,000

time 360 (30 years x 12 months)

rate 0.004666667 (5.6% annual rate divide into 12 months)

`500000 / (1-(1+0.00466666666666667)^(-360))/(0.00466666666666667) = C\\`

C $ 2,870.395

Next, we calculate the amortization on the first period:

payment less interest = amortization

$2,870.395 - $500,000 x 0.004666667 = $ 537.06

Now the value of this amortization over an 8 years period annuity:

`C * ((1+r)^(-time) -1)/(rate) = PV\\`

C $ 537.06

time 96 (8 years x 12 months)

rate 0.004666667

`537.061 * ((1+0.00466666666666667)^(96) -1)/(0.00466666666666667) = PV\\`

PV $64,848.3291

Last, the ballon payment: 500,000 - 64,848.33 = 435,151.67