Susan and ronald dugan agreed upon the price of 256,000 for their new home. They plan to make 30 percent down payment and financ

Question

2 months ago

5

e the rest at 7.5 persent for 20 years. What the total amount to be paid rounded to the nearest whole dollar?

1 answer:

babunello [11.8K] · Answer 1 · 2026-03-28T18:23:02+03:00

Answer:

The total amount due for purchasing the new home comes to $838,014.72

Step-by-step explanation:

Provided are:

The price set for the new house is $256,000

The down payment intended is 30% of the house price

Therefore, the down payment totals = 30% of $256,000

i.e. The down payment equals to $\dfrac{30}{100}$ × 256000

Or, The down payment price computes to $76,800

Next, the remaining amount is financed

Thus, The financing amount is p = $256000 - $76800 = $179,200

The interest rate applied = r = 7.5%

The duration for financing = t = 20 years

Let The Amount after 20 years of financing be $A

Let the overall sum payable for the new home = $B

Using Compound Interest

Amount = Principal × $(1+\dfrac{\textrm rate}{100})^{\textrm time}$

Or, A = p × $(1+\dfrac{\textrm r}{100})^{\textrm t}$

Or, A = $179,200 × $(1+\dfrac{\textrm 7.5}{100})^{\textrm 20}$

Or, A = $179,200 × $(1.075)^{\textrm 20}$

Or, A = $179,200 × 4.24785

∴ A = $761,214.72

Therefore,The Amount to be paid after 20 years of financing = A = $761,214.72

Subsequently

The final amount to be paid for the new home = Down payment total + The Amount to be paid after 20 years of financing

Or, B = $76,800 + A

Or, B = $76,800 + $761,214.72

Or, B = $838,014.72

Therefore, the overall amount due for the new home is rounded to $838,014.72 Answer