A group of private investors purchased a condominium complex for $4 million. They made an initial down payment of 12% and obtained financing for the balance. If the loan is to be amortized over 12 years at an interest rate of 13% /year compounded quarterlly, find the required quarterly payment. Please round the answer to the nearest cent.
A) $144,172.53
B) $143,175.06
C) $147,533.39
D) $145,809.68
E) $147,646.05

Question

A group of private investors purchased a condominium complex for $4 million. They made an initial down payment of 12% and obtained financing for the balance. If the loan is to be amortized over 12 years at an interest rate of 13% /year compounded quarterlly, find the required quarterly payment. Please round the answer to the nearest cent. ​
A) $144,172.53
B) $143,175.06
C) $147,533.39
D) $145,809.68
E) $147,646.05

Quizplus · Accepted Answer

Firstly, let's calculate the amount of the loan:

Down payment = 12% of $4,000,000 = $480,000
Loan amount = $4,000,000 - $480,000 = $3,520,000

Next, we need to find the quarterly interest rate:

Annual interest rate = 13%
Quarterly interest rate = 13%/4 = 0.0325

Finally, we can use the formula for amortization to find the quarterly payment:

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

where:
P = quarterly payment
r = quarterly interest rate
A = loan amount
n = number of quarterly payments

n = 12 years * 4 quarters per year = 48
r = 0.0325
A = $3,520,000

Plugging in the numbers, we get:

P = (0.0325 * $3,520,000) / (1 - (1+0.0325)^(-48))
P = $145,809.68

Rounding to the nearest cent, the answer is D) $145,809.68.

A Group of Private Investors Purchased a Condominium Complex for $4