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A basic arm is made for $200000 at an initial interest rate of 6 percent for...

A basic arm is made for $200000 at an initial interest rate of 6 percent for 30 years with an annual reset date. The borrower believes that the interest rate at the beginning of year 2 will increase to 7 percent.

(a) Assuming that a fully amortizing loan is made, what will the monthly payments be during year 1?

(b) Based on (a), what will the loan balance be at the end of year 1?

(c) Given that the interest rate is expected to be 7 percent at the beginning of year 2, what will the monthly payments be during year 2?

Solutions

Expert Solution

Sol:

Present value (PV) = $200,000

Interest rate (r) = 6% (Monthly) = 6%/12 = 0.50%

Period (nper) = 30 (Monthly) = 30 x 12 = 360

Monthly payment (PMT)

a) To determine monthly payments be during year 1: (Formula in excel sheet)

=PMT(rate,nper,pv,0)

=PMT(0.50%,360,200,000,0)

PMT = $1,199.10

PV 200000
Interest rate 0.50%
nper 360
Monthly payment (PMT) 1199.10

Therefore monthly payments be during year 1 is $1,199.10

b)

Interest rate (r) = 6% (Monthly) = 6%/12 = 0.50%

Period (nper) = 29 (Monthly) = 29 x 12 = 348

Monthly payment (PMT) = $1199.10

Loan balance (PV)

Based on (a), loan balance be at the end of year 1: (Formula in excel sheet)

= PV(rate,nper,PMT,0)

= PV(0.50%,348,1199.10,0)

PV = $197,543.80

PMT 1199.1
Interest rate 0.50%
nper 348
Loan balance (PV) 197543.80

Therefore loan balance be at the end of year 1 is $197,543.80

c)

Interest rate (r) = 7% (Monthly) = 7%/12 = 0.58333333%

Period (nper) = 29 (Monthly) = 29 x 12 = 348

PV = $197,543.80

Monthly payment (PMT)

Given that the interest rate is expected to be 7 percent at the beginning of year 2, monthly payments be during year 2 will be: (Formula in excel sheet)

=PMT(rate,nper,pv,0)

=PMT(0.58333333%,348,197,543.80,0)

PMT = $1327.75

PV 197543.8
Interest rate 0.58%
nper 348
Monthly payment (PMT) 1327.75

Therefore beginning of year 2, monthly payments be during year 2 will be $1327.75

jeff jeffy answered 1 year ago
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