Susan and ronald dugan agreed upon the price of 256,000 for their new home. they plan to make 30 percent down payment and finance the rest at 7.5 persent for 20 years. what the total amount to be paid rounded to the nearest whole dollar?

The total amount to be paid for new home is $838,014.72  

Step-by-step explanation:

Given as :

The price of the new house = $256,000

The down payment amount = 30% of house price

So, The down payment price =  30% of $256,000

i.e The down payment price =   × 256000

Or, The down payment price = $76,800

Now, rest amount is finance

So, The finance Amount = p = $256000 - $76800 = $179,200

The rate of interest applied = r = 7.5%

The time period of finance = t = 20 years

Let The Amount after 20 years of finance = $A

Let The total amount to be paid for new home = $B

Now, From Compound Interest

Amount = Principal ×

Or, A = p ×

Or, A = $179,200 ×

Or, A = $179,200 ×

Or, A = $179,200 × 4.24785

∴  A = $761,214.72

So,The Amount after 20 years of finance = A = $761,214.72

Now, Again

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

Or, B = $76,800 + A

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

Or, B = $838,014.72

So, The total amount to be paid for new home = B = $838,014.72

Hence, The total amount to be paid for new home is $838,014.72  Answer

the answer is:

the correct option:

b.

to solve the problem, we need to remember how to operate to simplify exponential expressions using the logarithms.

we are given the equation:

then, using placing logarith with base 7 on both sides of the equation, we have:

so, rounding the obtained result to two decimal places (nearest hundreth), we have:

hence, we have that the correct option:

b.

have a nice day!