Question

Question 3 of 5

Meghan received a loan of $7,200 at 5.50% compounded monthly. She settled the loan by making periodic payments at the end of every three months for 6 years, with the first payment made 3 years and 3 months from now. What was the size of the periodic payments?
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Question 4 of 5
James was receiving rental payments of $2,000 at the beginning of every month from the tenants of his commercial property. What would be the value of his property in the market if he wants to sell it, assuming a market capitalization rate of 4.50% compounded annually?
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Answer 1

To calculate the size of the periodic payments, we can use the formula for the present value of an annuity. The size of the periodic payments is approximately $349.89.

Step-by-step explanation:

To calculate the size of the periodic payments, we can use the formula for the present value of an annuity. The present value is equal to the periodic payment multiplied by the present value factor. In this case, the loan has a term of 6 years and the payments are made every 3 months, so there are a total of 24 payments. The interest rate is 5.50% compounded monthly, which means the monthly interest rate is 5.50% divided by 12.

The present value factor can be calculated using the formula:

Present Value Factor = (1 - (1 + r)^(-n)) / r

Where r is the monthly interest rate and n is the number of payments. Plugging in the values:

Present Value Factor = (1 - (1 + 0.055/12)^(-24)) / (0.055/12)

Calculating this expression gives us the value of approximately 20.6073. Now, we can solve for the periodic payment by dividing the loan amount by the present value factor:

Periodic Payment = $7,200 / 20.6073

Using a calculator, we find that the size of the periodic payments is approximately $349.89.

Answer 2

The size of the periodic payments for Meghan's loan is $463.97.

Step-by-step explanation:

To calculate the size of the periodic payments, we can use the formula for the future value of an annuity: FV = P * ((1 + r)^n - 1) / r, where FV is the future value, P is the periodic payment, r is the interest rate per period, and n is the number of periods.

In this case, the future value (FV) is the loan amount of $7,200, the interest rate (r) is 5.50% per year/12 (since it is compounded monthly), and the number of periods (n) is 6 years * 4 (since the payments are made every three months).

Plugging the values into the formula, we get:

FV = P * ((1 + 0.055/12)^(6*4) - 1) / (0.055/12)

Solving for P, we find that the size of the periodic payments is approximately $463.97 to the nearest cent.