Question

A homeowner planning a kitchen remodeling can afford a $900 monthly payment. How much can the homeowner borrow for 2 years at 6%, compounded monthly, and still stay within the budget? (Round your answer to the nearest cent.)

Answer 1

We can find the answer using the present value of the annuity formula:

PVA = A (1-(1+i/a)-") i/a

Where,
PVA = Present value of the annuity
A = Annuity or payment
i = Interest rate in decimal form (i.e 6% = 0.06)
n = Number of years
a = Number of payments in a year

Therefore,

$\small \textup{PVA} = \textup{900}\left [\frac{(1-(1+0.06/12)^{-2*12})}{0.06/12} \right ]$

= 900 (1-(1.005)-24) 0.005

$\small = \textup{900}\left [\frac{1-0.88718567}{0.005} \right ]$

$\small = \textup{900}\left [\frac{0.11281433}{0.005} \right ]$

$\small = \textup{900}\times 22.56287$

$\small = \$$20,306.58$

Therefore, the homeowner can borrow $20,306.58 and still stay within the budget.