Question

          Ms. Juliet bought a house for $360,000 exactly five years ago. After making a 20% down-payment, she borrowed the rest of the house payment in the form of a 15-year mortgage from her local cooperative credit union. She negotiated a mortgage rate of 3.5% APR with semi-annual compounding. She makes mortgage payments of an equal dollar amount every two weeks (i.e., biweekly), and her first mortgage payment was due two weeks after she signed the mortgage contract.

If Ms. Juliet can renegotiate a new 10-year mortgage rate of 2.5% APR with monthly compounding on her current mortgage balance, what will be her new biweekly mortgage payment?       

Answer 1

we have to calculate bi - weekly rate

Effective annual rate(EAR)  = (1 + (r/n))^n - 1

where r = APR

n = compounding periods

EAR = (1 + (3.5%/2))^2 - 1 = 3.5306%

(1 + x)^26 - 1 = 3.5306% (let x = bi-weekly rate)

so x = 0.1335%

Down payment = 20%

so balance = 360000*(1 - 20%) = 288,000

number of periods = 26 weeks*15years = 390

first we have to find monthly payments and balance of loan after 5 years

A B 1 Loan amount 2 Interest rate(bi-weekly) 3 Number of periods 4 biweekly payments 5 6 balance after 5 years 288000 0.134% 390 $947.86 208093.73

now we can find new bi - weekly payments:

New EAR = (1 + (2.5%/12))^12 - 1

= 2.53%

Bi - weekly rate = (1+2.53%)^(1/26) - 1

= 0.096%

Bi weekly payments:

А 1 Loan balance 2 interest rate 3 Number of periods 4 New Bi-weekly payments B 208093.73 0.096% 260 $904.89

so New Bi - weekly Payments = $904.89

Formulas will be as follows:

A B 1 Loan amount 288000 2. Interest rate(bi-weekly) =E5 3 Number of periods = 26*15 4 bi weekly payments =PMT(B2,B3,-B1,0) Сл 6 balance after 5 years --PV(B2,260,B4,0)

(E5 cell is interest rate = 0.1335%)

(formula for second part will be same as above Except number change)