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On January 1, 2019, ABC Corp. borrowed $81,000 by signing an installment loan.  The loan will be...

On January 1, 2019, ABC Corp. borrowed $81,000 by signing an installment loan.  The loan will be repaid in 20 equal payments, one at the beginning of each year.  The first payment is made on January 1, 2017. The interest rate for the loan is 10%. Calculate the annual payment required.  Show your final answer and show all the work to support your answer. Prepare the amortization table for the loan using the format covered in class.

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Answer #1

equal annual payment

= P * R * (1+R)n / (+r)n - 1

p = 81000

r= 0.10

n = 20years

As the first payment is made immediately

we would deduct 1 from n in numerator

= 81000 *0.10 * (1+0.10)20-1/ (1+0.10)20-1

=8100*[6.1159/5.7275]

=8649.29$

Period beginning balance Payment Principal [beginning balance-interest] interest beginning balance *10% ending balance [beginning balance - principal]
January 1,2019 81000 8649.29 8649.29 0.00 72350.71
January 1,2020 72350.71 8649.29 1414.22 7235.07 70936.49
January1,2021 70936.49 8649.29 1555.64 7093.65 69380.85
January1,2022 69380.85 8649.29 1711.20 6938.09 67669.65
January1,2023 67669.65 8649.29 1882.33 6766.96 65787.32
January1,2024 65787.32 8649.29 2070.56 6578.73 63716.76
January1,2025 63716.76 8649.29 2277.61 6371.68 61439.15
January1,2026 61439.15 8649.29 2505.38 6143.91 58933.77
January1,2027 58933.77 8649.29 2755.91 5893.38 56177.86
January1,2028 56177.86 8649.29 3031.50 5617.79 53146.36
January1,2029 53146.36 8649.29 3334.65 5314.64 49811.70
January1,2030 49811.70 8649.29 3668.12 4981.17 46143.58
January1,2031 46143.58 8649.29 4034.93 4614.36 42108.65
January1,2032 42108.65 8649.29 4438.43 4210.86 37670.22
January1,2033 37670.22 8649.29 4882.27 3767.02 32787.96
January1,2034 32787.96 8649.29 5370.49 3278.80 27417.46
January1,2035 27417.46 8649.29 5907.54 2741.75 21509.92
January1,2036 21509.92 8649.29 6498.30 2150.99 15011.62
January1,2037 15011.62 8649.29 7148.13 1501.16 7863.49
January1,2038 7863.49 8649.29 7862.94 786.35 0.00

there will be no interest in 1st year as the installment is paid immediately

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