Answer:
a) $2043.14
b) 22.19 years
c) $113,995.6
Step-by-step explanation:
Value of Mortgage ( P ) = $360,000,
Loan Tenure = 30 years
Annual Interest rate = 5.5% = 0.055
monthly interest rate ( m ) = 0.055 / 12 = 0.00458
number of payments ( n ) = 30 * 12 = 360
a) Determine Sara's monthly payment given that Sara pays continuously at a fixed amount
Monthly payments ( M ) = ( P * m ( 1 + m )^n ) / (( 1 + m )^n - 1 )
= ( 360,000 * 0.00458 ( 1.00458)^360 / ((1.00458)^360 - 1 )
= $2043.14
b) when she pays a n extra $300 every month determine time ( n ) when she can pay off the mortgage
i.e. M = 2034.14 + 300 = $2334.14
calculate the value of n from the equation below
M = ( P * m ( 1 + m )^n ) / (( 1 + m )^n - 1 )
n = - In | 1 -(( Pm) /M )) |/ In | 1 + m |
= -In | 1 - (( 360,000 * 0.00458) / 2334.14 )) | / 0.0045
= -In ( 1 - 0.70638436 ) / 0.0045
= 1.225 / 0.0046 = 266.30 months = 22.19 years
c) Determine how much Sara can save
Total amount paid using fixed monthly payment = 2043.14 * 30 * 12 = $735,530.4
Total amount paid by adding an extra $3000 each month
= 2334.14 * 22.19 * 12 = $621,534.80
amount saved = 735,530.4 - 621,534.80 = $113,995.6
