A bank just approved your small business loan for $20,000. The loan has an inter

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? $2,980.59 O $3,981.65 O $4,271.33 O $3,642.15 O $4,572.2:3 Halfway through the loan's life, what is the loan's remaining balance? O $11,122 O $11,901 O $15,288 O $17,342 O $15,557 What percentage of the total payments made during the first five years will be made toward interest? 56.13% 49.44% 54.56% 41.53% 45.66% O

Explanation / Answer

Find the equal installment:

PV of annuity = P*[(1-(1+r)^(-n)) / r]

P - Periodic payment = ?

r - rate per period = 0.08

n - number of periods = 10

20000 = P*((1-(1+0.08)^(-10)) / 0.08)

P = $2980.59

Construct the amortization table as below:

- Annual loan payment = $2980.59

- At the end of 5th year, the loan balance is $11900.63, which is $11901

- Sum the first 5 rows from column 'Interest'

Total interest paid during 5 payments = 1600+ 1489.55+1370.27 + 1241.44 + 1102.31 = 6803.58

Total payment made = 5*2980.59 = 14902.949

% of total payments made during the first 5 years towards interest = 6803.58/14902.949 = 0.4566 = 45.66%

Year Beginning balance Annual payment Interest = Beginning Balance *0.08 Principal = Annual payment - Amount to interest Ending Balance = Beginning balance - Principal 1 20000 2980.59 1600.00 1380.59 18619.41 2 18619.41 2980.59 1489.55 1491.04 17128.37 3 17128.37 2980.59 1370.27 1610.32 15518.05 4 15518.05 2980.59 1241.44 1739.15 13778.91 5 13778.91 2980.59 1102.31 1878.28 11900.63 6 11900.63 2980.59 952.05 2028.54 9872.09 7 9872.09 2980.59 789.77 2190.82 7681.27 8 7681.27 2980.59 614.50 2366.09 5315.18 9 5315.18 2980.59 425.21 2555.38 2759.81 10 2759.81 2980.59 220.78 2759.81 0.00

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