Question

Geoffrey decides not to buy the car mentioned earlier. Instead, he is now considering a food delivery service "You, bars, meats" that his friend Gillian has recently started. Gillian has agreed that for a single payment of $52,000 today to help her launch her business, she will provide all the delivery services that Geoffrey needs for his business for the next 5 years. Geoffrey is considering borrowing the full amount from his business account.

Suppose that Geoffrey makes level quarterly repayments over the coming 5 years, the first payment being exactly 3 months from today. Again, the interest rate on Geoffrey's account is 4.5% p.a. effective.

How much interest does Geoffrey pay in the first year?

Answer 1

Loan amount = $52,000

Loan Period = 5 years

Payment Frequency = Quarterly

Annual Effective Interest Rate = 4.5%

Annual Nominal Interest Rate for Quarterly compounding can be calculated from Annual Effective Rate by using the NOMINAL function in spreadsheet

NOMINAL (Effective Rate, Periods per year)

Where, Effective Rate = Annual Effective Rate = 4.5%

Periods per year = number of compounding periods per year = 4

Annual Nominal Interest Rate = NOMINAL (4.5%, 4) = 4.425996%

Quarterly Interest Rate = Annual Nominal Interest Rate / 4 = 4.425996%/4 = 1.106499%

The Quarterly loan payment can be calculated using the PMT function in spreadsheet

PMT(rate, number of periods, present value, future value, when-due)

Where, rate = quarterly interest rate = 1.106499%

number of periods = no.of quarterly periods = 5*4 = 20

present value = loan amount = $52,000

future value = loan amount after the loan period = 0

when-due = when is the payment made each quarter = end = 0

Quarterly loan payment = PMT(1.106499%, 20, 52000, 0, 0) = $2,912.59

Total Payments made by Geoffrey in the first year = Quarterly payment * 4 = $2,912.59*4 = $11,650.37

Principal Payment made in first year = Principal balance at the start of the loan - principal balance after 1 year

= $52,000 - $42,494.83 = $9,505.17

Interest payment made in first year = total payments made in first year - principal payment made in first year

= $11,650.37 - $9,505.17 = $2,145.20