Question

Stuart is considering a 3/27 balloon mortgage with an interest rate of 4.4to purchase a house for $268,000. What will be his balloon payment at the end of 3 years?

Answer 1

$ 251,619.37

Explanation:

Given that :

Loan = $ 268,000

Interest rate = 4.4 % per annum

4.4%/12 months = 0.366% per month

`$3/27$` :
`$3$` years to pay and
`27` years amortization

`27` years x 12 months =
`324` months

Calculating the amount for he monthly amortization,

`$A=P * (r(1+r)^n)/((1+r)^n-1)$`

`$A=268,000 * (0.00366(1+0.0366)^(324))/((1+0.00366)^(324)-1)$`

`$A=268,000 * (0.0119)/(2.266)$`

A = 1407.41

Therefore, the future value is given by :

`$FV=PV(1+r)^n-P\left[((1+r)^n-1)/(r)\right]$`

where, FV = future value ( balloon balance)

PV = present value (original balance)

P = payment

r = rate per payment

n = number of payments

`$FV=268,000(1+0.00366)^(36)-1407.41\left[((1+0.00366)^(36)-1)/(0.00366)\right]$`

`$FV = 305670.10- 54050.73 $`

FV = 251619.37

Therefore, Stuart's balloon payment will be $ 251,619.37