(a) To calculate the quarterly interest payment for the interest-only loan, we first need to find the annual interest. This is done by multiplying the loan amount by the interest rate:

$275,000 * 5.2% = $14,300

Since there are 4 quarters in a year, we divide the annual interest by 4 to get the quarterly interest payment:

$14,300 / 4 = $3,575

So, the quarterly interest payment for the interest-only loan is $3,575.

(b) The total cost of the interest-only loan is the sum of the interest paid over the 5 years and the principal amount. The interest paid over 5 years is $14,300 * 5 = $71,500. So, the total cost of the loan is $71,500 + $275,000 = $346,500.

The total amount paid into the sinking fund is the monthly payment multiplied by the number of months, which is $4116.44 * 60 = $247,986.40.

So, the total cost of the interest-only loan and the sinking fund is $346,500 + $247,986.40 = $594,486.40.

(c) (i) To calculate the value of the sinking fund at the end of the first year, we use the formula for the future value of an annuity:

FV = P * [(1 + r/n)^(nt) - 1] / (r/n)

where P is the monthly payment, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years. Plugging in the given values, we get:

FV = $4116.44 * [(1 + 4.3%/12)^(12*1) - 1] / (4.3%/12) = $50,639.91

(ii) The interest earned by the sinking fund in the first year is the value of the fund at the end of the year minus the total amount paid into the fund during the year, which is $50,639.91 - $4116.44*12 = $1,403.67.

(iii) The association can expect the sinking fund to earn more interest in the second year than in the first year because the fund will have a larger balance at the start of the second year. The interest earned by the fund is proportional to its balance, so a larger balance will result in more interest.

Question

(a) To calculate the quarterly interest payment for the interest-only loan, we first need to find the annual interest. This is done by multiplying the loan amount by the interest rate:

$275,000 * 5.2% = $14,300

Since there are 4 quarters in a year, we divide the annual interest by 4 to get the quarterly interest payment:

$14,300 / 4 = $3,575

So, the quarterly interest payment for the interest-only loan is $3,575.

(b) The total cost of the interest-only loan is the sum of the interest paid over the 5 years and the principal amount. The interest paid over 5 years is $14,300 * 5 = $71,500. So, the total cost of the loan is $71,500 + $275,000 = $346,500.

The total amount paid into the sinking fund is the monthly payment multiplied by the number of months, which is $4116.44 * 60 = $247,986.40.

So, the total cost of the interest-only loan and the sinking fund is $346,500 + $247,986.40 = $594,486.40.

(c) (i) To calculate the value of the sinking fund at the end of the first year, we use the formula for the future value of an annuity:

FV = P * [(1 + r/n)^(nt) - 1] / (r/n)

where P is the monthly payment, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years. Plugging in the given values, we get:

FV = $4116.44 * [(1 + 4.3%/12)^(12*1) - 1] / (4.3%/12) = $50,639.91

(ii) The interest earned by the sinking fund in the first year is the value of the fund at the end of the year minus the total amount paid into the fund during the year, which is $50,639.91 - $4116.44*12 = $1,403.67.

(iii) The association can expect the sinking fund to earn more interest in the second year than in the first year because the fund will have a larger balance at the start of the second year. The interest earned by the fund is proportional to its balance, so a larger balance will result in more interest.

Knowee AI · Accepted Answer