A couple purchased a home 5 years ago with a 20-year mortgage for $50,000 at an interest rate of 6% compounded monthly. The home is now valued at $90,000.
A) How much are the couple's monthly payments?
B)What is their balance after 7 years and how much equity is in their new home now?
C) How much will the finance charge (total interest paid) be?
i = .06/12 = .005
n = 20(12) = 240
PV = 50,000
paym = ??
paym( 1 - 1.005^-240)/.005 = 50,000
payment = $358.22
after 7 years:
balance of mortgage
= 50000(1.005)^84 - 358.22(1.005^84 - 1)/.005
= $38,737.12
Since the current value is 90,000 but they still owe 38,737.12
the equity would be 90000-38737.12
= 51,262.88
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To answer these questions, we'll need to use the formula for calculating monthly mortgage payments, the formula for calculating compound interest, and the formula for calculating equity.
A) To find the monthly mortgage payments, we can use the formula for the payment on a loan:
P = (Pv * r * (1 + r)^n) / ((1 + r)^n - 1)
where:
P = monthly payment
Pv = present value (loan amount)
r = monthly interest rate
n = number of monthly payments
In this case, the present value (Pv) is $50,000, the interest rate (r) is 6% (or 0.06), and the number of monthly payments (n) is 20 years * 12 months = 240 months.
Plugging these values into the formula:
P = (50000 * 0.005 * (1 + 0.005)^240) / ((1 + 0.005)^240 - 1)
Using a calculator, the monthly payment (P) is approximately $372.86.
B) To find the balance after 7 years and the equity in the new home, we need to calculate the remaining loan balance and subtract it from the current home value.
First, we need to calculate the number of payments made after 7 years, which is 7 years * 12 months = 84 months.
Next, we can use the compound interest formula to calculate the remaining loan balance:
A = P * (1 + r)^n
where:
A = final amount or balance
P = initial amount or loan amount
r = monthly interest rate
n = number of periods
In this case, the initial amount (P) is $50,000, the monthly interest rate (r) is 0.005 (6% divided by 12), and the number of periods (n) is 84.
Plugging in these values:
A = 50000 * (1 + 0.005)^84
Using a calculator, the remaining loan balance after 7 years is approximately $36,195.49.
To calculate the equity in the new home, we subtract the remaining loan balance from the current home value:
Equity = Current Home Value - Remaining Loan Balance
Equity = $90,000 - $36,195.49
The equity in their new home after 7 years is approximately $53,804.51.
C) To calculate the finance charge or total interest paid, we can subtract the initial loan amount from the total amount repaid over the 20-year mortgage term.
Total Amount Repaid = Monthly Payment * Number of Payments
Total Interest Paid = Total Amount Repaid - Loan Amount
In this case, the monthly payment is $372.86, and the number of payments is 240.
Total Amount Repaid = 372.86 * 240
Total Interest Paid = (372.86 * 240) - 50000
Using a calculator, the total interest paid is approximately $29,285.58.