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You have taken out a loan of 2,000,000 to buy a house on Easter Island. The loan is an annuity loan of 20 years with fixed annual repayments, and the first repayment takes place one year after borrowing. The interest rate is 4% per annum.

a. What is the annual term amount?
b. how much of the initial repayment is interest and how mush are installments?

1 Answer

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Final answer:

The annual term amount for the annuity loan is approximately $169,648.39. The interest portion of the initial repayment is $80,000, and the amount dedicated to installments is $89,648.39.

Step-by-step explanation:

To calculate the annual term amount in an annuity loan, we can use the present value of an annuity formula. The formula is as follows:

Annual Term Amount = PV / ((1 - (1 + r)^(-n)) / r),

Where PV is the loan amount, r is the interest rate per period, and n is the number of periods.

In this case, the loan amount is $2,000,000, the interest rate is 4% per annum, and the loan term is 20 years. Let's plug these values into the formula:

Annual Term Amount = 2,000,000 / ((1 - (1 + 0.04)^(-20)) / 0.04).

Calculating this, we find that the annual term amount is approximately $169,648.39.

To find out how much of the initial repayment is interest and how much are installments, we can calculate the interest portion and subtract it from the annual term amount. The interest portion can be calculated by multiplying the loan amount by the interest rate:

Interest Portion = Loan Amount * Interest Rate = 2,000,000 * 0.04 = 80,000.

Subtracting the interest portion from the annual term amount, we get:

Installment = Annual Term Amount - Interest Portion = 169,648.39 - 80,000 = 89,648.39.

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