a) To calculate the amount of the annual principal repayment, we need to divide the total loan amount by the number of years over which the loan will be repaid.

Annual principal repayment = Total loan amount / Number of years

Annual principal repayment = $510,000 / 7

Annual principal repayment = $72,857.14

Therefore, the amount of the annual principal repayment is $72,857.14.

b) To calculate the stream of interest payments, we need to multiply the outstanding loan balance at the beginning of each year by the interest rate.

Outstanding loan balance at the beginning of year 1 = $510,000

Interest payment in year 1 = $510,000 x 7.5% = $38,250

Outstanding loan balance at the beginning of year 2 = $510,000 - $72,857.14 = $437,142.86

Interest payment in year 2 = $437,142.86 x 7.5% = $32,785.71

We can continue this process for each year until the loan is fully repaid.

Therefore, the stream of interest payments is:

Year 1: $38,250
Year 2: $32,785.71
Year 3: $27,321.43
Year 4: $21,857.14
Year 5: $16,392.86
Year 6: $10,928.57
Year 7: $5,464.29

c) To calculate the stream of total annual repayments, we need to add the annual principal repayment and the interest payment for each year.

Total annual repayment = Annual principal repayment + Interest payment

Year 1: $72,857.14 + $38,250 = $111,107.14
Year 2: $72,857.14 + $32,785.71 = $105,642.86
Year 3: $72,857.14 + $27,321.43 = $100,178.57
Year 4: $72,857.14 + $21,857.14 = $94,714.28
Year 5: $72,857.14 + $16,392.86 = $89,250
Year 6: $72,857.14 + $10,928.57 = $83,785.71
Year 7: $72,857.14 + $5,464.29 = $78,321.43

Therefore, the stream of total annual repayments is:

Year 1: $111,107.14
Year 2: $105,642.86
Year 3: $100,178.57
Year 4: $94,714.28
Year 5: $89,250
Year 6: $83,785.71
Year 7: $78,321.43

Question

a) To calculate the amount of the annual principal repayment, we need to divide the total loan amount by the number of years over which the loan will be repaid.

Annual principal repayment = Total loan amount / Number of years

Annual principal repayment = $510,000 / 7

Annual principal repayment = $72,857.14

Therefore, the amount of the annual principal repayment is $72,857.14.

b) To calculate the stream of interest payments, we need to multiply the outstanding loan balance at the beginning of each year by the interest rate.

Outstanding loan balance at the beginning of year 1 = $510,000

Interest payment in year 1 = $510,000 x 7.5% = $38,250

Outstanding loan balance at the beginning of year 2 = $510,000 - $72,857.14 = $437,142.86

Interest payment in year 2 = $437,142.86 x 7.5% = $32,785.71

We can continue this process for each year until the loan is fully repaid.

Therefore, the stream of interest payments is:

Year 1: $38,250 
Year 2: $32,785.71 
Year 3: $27,321.43 
Year 4: $21,857.14 
Year 5: $16,392.86 
Year 6: $10,928.57 
Year 7: $5,464.29

c) To calculate the stream of total annual repayments, we need to add the annual principal repayment and the interest payment for each year.

Total annual repayment = Annual principal repayment + Interest payment

Year 1: $72,857.14 + $38,250 = $111,107.14 
Year 2: $72,857.14 + $32,785.71 = $105,642.86 
Year 3: $72,857.14 + $27,321.43 = $100,178.57 
Year 4: $72,857.14 + $21,857.14 = $94,714.28 
Year 5: $72,857.14 + $16,392.86 = $89,250 
Year 6: $72,857.14 + $10,928.57 = $83,785.71 
Year 7: $72,857.14 + $5,464.29 = $78,321.43

Therefore, the stream of total annual repayments is:

Year 1: $111,107.14 
Year 2: $105,642.86 
Year 3: $100,178.57 
Year 4: $94,714.28 
Year 5: $89,250 
Year 6: $83,785.71 
Year 7: $78,321.43

Knowee AI · Accepted Answer