Question 1162035: A young couple is ready to buy their first home. They have 29,000 dollars for a down payment, and their budget can accommodate a monthly mortgage payment of 1,150 dollars. What is the most expensive home they can buy if they can borrow money for 30 years at 6.6%, compounded monthly?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! their down payment is 29,000 dollars.
their budget can accommodate a monthly mortgage of 1,150 dollars.
the mortgage is for 30 years at 6.6% per year compounded monthly.
payments are assumed to be at the end of each month.
using a financial calculator, i do the following:
present value = 0
future value = 0
interest rate per month = 6.6% / 12 = .55% per month.
number of months equals 30 years * 12 = 360 months.
payments are 1,150 made at the end of each month.
calculator computes the present value to be equal to 180,064.84 rounded to the nearest penny.
add the down payment to that to get 209,064.84.
that's the most expensive home he can buy with his down payment and that mortgage.
you can also solve this by formula.
the formula is:
PRESENT VALUE OF AN ANNUITY WITH END OF TIME PERIOD PAYMENTS
p = (a*(1-1/(1+r)^n))/r
p is the present value of the annuity.
a is the annuity.
r is the interest rate per time period.
n is the number of time periods.
in this formula:
a = 1150
r = 6.6% / 12 / 100 = .0055
n = 30 * 12 = 360
formula becomes:
p = (1150*(1-1/(1+.0055)^360))/.0055 = 180,064.8433
round to nearest penny and add 29,000 to get 209,064.84
formula and calculator give you the same results.
calculator used percent.
formula used rate, which is percent / 100.
|
|
|
