Question

A bank just approved your small business loan for $20,000. The loan has an interest rate of 8.0% and will be repaid with 10 end-of-year payments. What is the required annual loan payment?

Halfway through the loan's life, what is the loan’s remaining balance?

What percentage of the total payments made during the first five years will be made toward interest?

Answer 1

Formula for calculating periodic interest payment in amortised loans is given as:

P= (r*PV)/(1-(1+r)^-n); where P is periodic payment, r is interest rate per period, PV is loan amount and n is number of periods.

So, P= (8%*20000)/(1-(1+8%)^-10)

P= $2980.59

So, required annual loan payment is $2980.59.

For the first payment, interest part= (8%*20000)= $1600. So, Principal part will be 2980.59-1600= 1380.59. Remaining Loan balance will be 20000-1380.59= 18619.41

Similarly, For the second payment, interest part= (8%*18619.41)= $1489.55. So, Principal part will be 2980.59-1489.55= 14.81.04 Remaining Loan balance will be 18619.41-1491.04= 17128.37

For the third payment, interest part= (8%*17128.37)= $1370.27. So, Principal part will be 2980.59-1370.27= 1610.32 Remaining Loan balance will be 17128.37-1610.32= 15518.05

For the fourth payment, interest part= (8%*15518.05)= $1241.44. So, Principal part will be 2980.59-1241.44= 17.39.15 Remaining Loan balance will be 15518.05-1739.15= 13778.90

For the fifth payment, interest part= (8%*13778.90)= $1102.31. So, Principal part will be 2980.59-1102.31= 1878.28 Remaining Loan balance will be 13778.90-1878.28= 11900.62

So, Halfway through the loan's life, which is 5 year, the loan's remaining balance is $11900.62

Out of the total payment of (5*2980.59)= $14902.95 for the first 5 years, the interest payments are 1600+1489.55+1370.27+1241.44+1102.31= $6803.57.

So, Percentage of the interest part= 6803.57/14902.95= 45.65%

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