Answer:
- monthly payment: $2998.32
- total investment: $929,496
Explanation:
When the interest is compounded a different number of times per year than payments are made, it is necessary to find an equivalent interest rate to apply to each payment.
For this purpose, we can use the formula ...
r = (1 +R/n)^(n/p) -1
where R is the nominal annual rate, n is the number of times interest is compounded per year, p is the number of payments made per year, and r is the effective monthly interest rate.
Putting the given numbers into this formula, we find ...
r = (1 +.04/2)^(2/12) -1 ≈ 0.00330589032
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We can use this value of r in the amortization formula to find the monthly payment for a loan of $600,000 -30,000 = $570,000. That formula is ...
A = Pr/(1 -(1+r)^-n)
where P is the principal amount of the loan, r is the monthly interest rate, and n is the number of months of the loan.
Using the values for this loan, we find the payment to be ...
A = $570,000·0.00330589032/(1 -1.00330589033^-300) ≈ $2998.32
The monthly payment on the loan is $2998.32.
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The total amount of the 300 monthly payments is ...
loan repayment amount = 300·$2998.32 = 899,496
This amount is added to the down payment to find the total investment:
total investment = $30,000 +899,496 = $929,496