Shannon finances $189,000 with a 20/7 balloon mortgage at 6.25%. How much will she pay for principal and interest over the life of the loan?
To calculate the total amount Shannon will pay for principal and interest over the life of the loan, we first need to determine the terms of the loan.
The 20/7 balloon mortgage suggests that Shannon will make fixed monthly payments for 20 years (240 months) based on a 7-year (84 months) amortization schedule. After making these payments for 7 years, the remaining principal balance will be due as a balloon payment.
Here's how we can calculate the total amount paid for the principal and interest:
Step 1: Calculate the monthly payment for the amortization period.
The loan amount is $189,000.
The annual interest rate is 6.25%.
The amortization period is 7 years, or 84 months.
Using the formula for calculating the monthly payment on a fixed-rate loan:
M = P * (r(1+r)^n) / ((1+r)^n - 1)
Where:
M = Monthly payment
P = Loan amount
r = Monthly interest rate
n = Number of payments
Calculating the monthly payment for the amortization period:
r = 6.25% / 12 = 0.0052083 (monthly interest rate)
n = 84 (number of payments)
P = $189,000
M = 189,000 * (0.0052083 * (1 + 0.0052083)^84) / ((1 + 0.0052083)^84 - 1)
M ≈ $2,461.71
Step 2: Calculate the total amount paid over the amortization period.
Total amount paid = Monthly payment * Number of payments
Total amount paid = $2,461.71 * 84
Total amount paid ≈ $206,754.84
So, Shannon will pay approximately $206,754.84 in principal and interest over the life of the loan.
To determine how much Shannon will pay for principal and interest over the life of the loan, we need to calculate the monthly payment first. A balloon mortgage typically has lower monthly payments, but the remaining balance is due in full at the end of the loan term.
Step 1: Convert the interest rate from a percentage to a decimal.
The interest rate is 6.25%, which is equivalent to 0.0625 (6.25/100).
Step 2: Calculate the monthly interest rate.
Take the annual interest rate (0.0625) and divide it by 12 (number of months in a year). The monthly interest rate is approximately 0.00521 (0.0625/12).
Step 3: Determine the number of monthly payments.
A 20/7 balloon mortgage means that Shannon will make monthly payments for 20 years (240 months), but the remaining balance will be due in full after 7 years (84 months). So, the total loan term is 84 months.
Step 4: Calculate the monthly payment using the balloon mortgage formula.
We can use the formula for fixed-rate amortizing mortgages:
Monthly Payment = Principal * (Monthly Interest Rate / (1 - (1 + Monthly Interest Rate)^[-Number of Monthly Payments]))
Substituting the values in the formula:
Principal = $189,000
Monthly Interest Rate = 0.00521
Number of Monthly Payments = 84
Monthly Payment = $189,000 * (0.00521 / (1 - (1 + 0.00521)^-84))
Using a calculator, we can evaluate this expression to find the monthly payment.
Step 5: Calculate the total amount paid in principal and interest.
Multiply the monthly payment by the total number of payments.
Total Amount Paid = Monthly Payment * Number of Monthly Payments
Calculating this will give us the final answer.
Please note that the above calculation assumes no additional fees or expenses related to the mortgage.
Not totally familiar with US mortgage laws, since they differ slightly from my Canadian laws, but I'll take a shot
we need the monthly payment over a 20 year period:
i = .0625/12 = .00520833... ( I store that to keep accuracy)
n = 20(12) = 240
paym( 1 - 1.00520833..^-240)/.005208333 ... = 189000
I got paym = $1381.45
so now we need the balance after 7 years
outstanding balance
= 189000(1.005208333..)^84 - 1381.45(1.005208333^84 - 1)/.00520833..
= $147,291.59
see what you can do with that.