A group of private investors purchased a condominium complex for $2 million. They made an initial down payment of 15% and obtained financing for the balance. The loan is to be amortized over 13 years at an interest rate of 15% per year compounded quarterly. (Round your answers to the nearest cent.)
What is the required quarterly payment?
$
Incorrect: Your answer is incorrect.
How much total interest will be paid on the loan?
$
Incorrect: Your answer is incorrect.
amount to be mortgaged = 2000000(.85) = .... (A)
i = .15/4 = .0375
n = 13(4) = 52
2000000(.85) = P(1 - 1.0375^-52)/.0375
solve for P, I get 74,774.89, what did you get ?
So what was your final answer?
Well, you know what they say about interest rates... they can be pretty "complex" sometimes! But don't worry, I'll help you out with this math problem.
To find the required quarterly payment, we need to calculate the loan amount. The down payment was 15% of $2 million, which means it was $300,000. So, the loan amount is $2 million minus $300,000, which is $1,700,000.
Now, let's calculate the quarterly payment using the formula for an amortized loan:
Payment = (Loan Amount * Quarterly Interest Rate) / (1 - (1 + Quarterly Interest Rate)^(-Number of Payments))
The quarterly interest rate is the annual interest rate divided by 4 (since we're compounding quarterly). So, the quarterly interest rate is 15% divided by 4, which is 0.15/4 = 0.0375.
The number of payments is the number of years multiplied by 4 (since there are 4 quarters in a year). So, the number of payments is 13 * 4 = 52.
Now plug in these values into the formula:
Payment = ($1,700,000 * 0.0375) / (1 - (1 + 0.0375)^(-52))
Calculating that out gives us a quarterly payment of approximately $55,369.73.
Now, let's move on to the total interest paid on the loan. To find that, we'll need to calculate the total payments made over the 13-year period and subtract the loan amount.
Total Payments = Payment * Number of Payments
Total Interest = Total Payments - Loan Amount
Using the values we calculated earlier:
Total Payments = $55,369.73 * 52 = $2,874,370.96
Total Interest = $2,874,370.96 - $1,700,000 = $1,174,370.96
So, the total interest paid on the loan will be approximately $1,174,370.96. Hope that helps!
To find the required quarterly payment, we need to calculate the loan amount and then use the loan amortization formula.
First, calculate the loan amount by subtracting the initial down payment from the purchase price:
Loan Amount = Purchase Price - Down Payment = $2,000,000 - (15% * $2,000,000) = $2,000,000 - $300,000 = $1,700,000.
Next, we can use the loan amortization formula:
PMT = (r * PV) / (1 - (1 + r)^(-n * t))
Where:
PMT = Required quarterly payment
r = Interest rate per quarter (15% per year compounded quarterly = 15% / 4 quarters = 0.15 / 4 = 0.0375)
PV = Present value of the loan ($1,700,000)
n = Number of times interest is compounded per year (quarterly = 4)
t = Number of years (13)
Plugging in the values into the formula, we get:
PMT = (0.0375 * $1,700,000) / (1 - (1 + 0.0375)^(-4 * 13))
PMT = $63,687.46
Therefore, the required quarterly payment is approximately $63,687.46.
Now, let's calculate the total interest paid on the loan. This can be done by multiplying the quarterly payment by the total number of payments and then subtracting the loan amount:
Total Interest Paid = (PMT * n * t) - PV
Total Interest Paid = ($63,687.46 * 4 * 13) - $1,700,000
Total Interest Paid = $3,302,530.12 - $1,700,000
Total Interest Paid = $1,602,530.12
Therefore, the total interest paid on the loan is approximately $1,602,530.12.