Sarah secured a bank loan of $200,000 for the purchase of a house. The mortgage is to be amortized through monthly payments for a term of 15 yr, with interest rate of 6%/year compounded monthly on the unpaid balance. She plans to sell her house in 5 yr. How much will Sarah still owe on her house?

Well, isn't it fascinating how houses and mortgages can turn our lives into a never-ending math problem? But fear not, I'm here to bring some fun to the equation!

Let's calculate, shall we? The loan amount is $200,000. The term is 15 years, but Sarah plans to sell the house in 5 years. So, we need to figure out how much will be left on the mortgage after 5 years.

To determine this, we need to find out the monthly payment first. Using a fancy formula, we can calculate that to be approximately $1,687.71 per month.

Now, let the countdown begin! In 5 years, Sarah will have made 60 monthly payments. But wait, there's interest too! At a 6% annual interest rate compounded monthly, the remaining balance after 5 years will be approximately...drumroll, please...$152,259.74!

So, Sarah will still owe around $152,259.74 on her house by the time she decides to sell it. Remember, these calculations are an estimate, so make sure to consult with a financial expert before making any decisions. Good luck, Sarah!

To calculate how much Sarah will still owe on her house after 5 years, we need to use the amortization formula:

M = P * (r * (1 + r)^n) / ((1 + r)^n - 1)

Where:
M = Monthly payment
P = Principal amount of the loan
r = Monthly interest rate
n = Number of monthly payments

First, let's calculate the monthly interest rate:
r = annual interest rate / 12 months
r = 6% / 12
r = 0.06 / 12
r = 0.005

Next, let's calculate the total number of monthly payments:
n = term in years * 12 months
n = 15 * 12
n = 180

Let's substitute the given values into our formula:

M = 200,000 * (0.005 * (1 + 0.005)^180) / ((1 + 0.005)^180 - 1)

Using a calculator or spreadsheet, we can find that the monthly payment is approximately $1,687.71.

Now, let's calculate the remaining balance after 5 years. Since Sarah made monthly payments for 5 years, the number of remaining payments would be:

Remaining payments = total number of payments - (term in years * 12)
Remaining payments = 180 - (5 * 12)
Remaining payments = 180 - 60
Remaining payments = 120

To calculate the remaining balance, we can use the formula:

Remaining balance = (M * ((1 + r)^n - (1 + r)^p)) / r

Where:
M = Monthly payment
r = Monthly interest rate
n = Total number of monthly payments
p = Number of payments made

Substituting the given values:

Remaining balance = (1,687.71 * ((1 + 0.005)^180 - (1 + 0.005)^120)) / 0.005

Using a calculator or spreadsheet, we can find that the remaining balance after 5 years is approximately $170,593.38.

Therefore, Sarah will still owe around $170,593.38 on her house after 5 years.

To determine how much Sarah will still owe on her house after 5 years, we need to calculate the remaining unpaid balance on the mortgage.

Step 1: Calculate the number of monthly payments made over the 5-year period.
Since there are 12 months in a year and Sarah plans to sell the house after 5 years, the total number of monthly payments made would be 12 * 5 = 60.

Step 2: Calculate the monthly interest rate.
The annual interest rate is 6%, compounded monthly. To find the monthly interest rate, we divide the annual rate by 12. Hence, the monthly interest rate would be 6% / 12 = 0.5%.

Step 3: Calculate the monthly payment amount.
To calculate the monthly payment amount, we can use the formula for the monthly payment on an amortized loan. The formula is:

M = P * r * (1 + r)^n / ((1 + r)^n - 1)

Where:
M is the monthly payment amount,
P is the loan principal amount ($200,000),
r is the monthly interest rate (0.5%),
n is the number of monthly payments (60).

Plugging in the values, we get:
M = 200,000 * 0.005 * (1 + 0.005)^60 / ((1 + 0.005)^60 - 1)
≈ $1,581.60 (rounded to two decimal places)

Step 4: Calculate the remaining balance on the mortgage.
To find the remaining balance on the mortgage after 5 years, we subtract the total amount paid (monthly payment * number of payments) from the original loan amount.

Total amount paid = Monthly payment amount * Number of payments
= $1,581.60 * 60
= $94,896.00

Remaining balance = Original loan amount - Total amount paid
= $200,000 - $94,896.00
= $105,104.00

Therefore, Sarah will still owe approximately $105,104.00 on her house after 5 years.

payment = ?

n = 180
i = .06/12 = .005
200000 = paym( 1 - 1.005^-180)/.005
paym = 1687.71

balance after 5 years
= 200000(1.005)^60 - 1687.71(1.005^60 - 1)/.005
=269770.03 - 117751.83
= 152018.20