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The residents’ association of a retirement village needs $275 000 to upgrade the village’s facilities.The association obtains a 5-year, interest-only loan for $275 000 that charges a flat interest rate of5.2% per annum.(a) Calculate the quarterly interest payment for the interest-only loan.(1 mark)In order to repay the loan, the association sets up a sinking fund and plans to make monthlypayments of $4116.44 over the 5 years. The sinking fund earns interest at a rate of 4.3% per annum,compounded monthly.(b) Calculate the total cost of the interest-only loan and the sinking fund

Question

The residents’ association of a retirement village needs 275000toupgradethevillage’sfacilities.Theassociationobtainsa5−year,interest−onlyloanfor275 000 to upgrade the village’s facilities.The association obtains a 5-year, interest-only loan for 275 000 that charges a flat interest rate of5.2% per annum.(a) Calculate the quarterly interest payment for the interest-only loan.(1 mark)In order to repay the loan, the association sets up a sinking fund and plans to make monthlypayments of $4116.44 over the 5 years. The sinking fund earns interest at a rate of 4.3% per annum,compounded monthly.(b) Calculate the total cost of the interest-only loan and the sinking fund

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Solution

(a) To calculate the quarterly interest payment for the interest-only loan, we first need to find the annual interest.

The formula for calculating the annual interest is:

Principal Amount * Interest Rate = Annual Interest

So, 275,000∗5.2275,000 * 5.2% = 14,300

Since the interest is paid quarterly, we divide the annual interest by 4:

14,300/4=14,300 / 4 = 3,575

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

(b) To calculate the total cost of the interest-only loan and the sinking fund, we first need to find the total interest paid over the 5 years and the total amount paid into the sinking fund.

The total interest paid over 5 years is:

Annual Interest * Loan Term = Total Interest

So, 14,300∗5=14,300 * 5 = 71,500

The total amount paid into the sinking fund is:

Monthly Payment * Number of Months = Total Sinking Fund Payments

So, 4116.44∗60=4116.44 * 60 = 247,586.4

The total cost of the interest-only loan and the sinking fund is the sum of these two amounts:

71,500+71,500 + 247,586.4 = $319,086.4

So, the total cost of the interest-only loan and the sinking fund is $319,086.4.

This problem has been solved

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