Problem 4-30 Loan Amortization Your company is planning to borrow $2 million on a 5-year, 8%,...

Problem 4-30
Loan Amortization

Your company is planning to borrow $2 million on a 5-year, 8%, annual payment, fully amortized term loan. What fraction of the payment made at the end of the second year will represent repayment of principal? Round your answer to two decimal places.

Solutions

Expert Solution

The formula for calculating the payment amount is shown below:

A = P * (r * (1 + r)ⁿ / (1 + r)ⁿ - 1)

where, A is the annual amount. P is the initial loan amount = $2000000, r is the rate of interest = 8% = 0.08 and n is the time period = 5 years

Now, putting these values in the above formula, we get,

A = $2000000 * (0.08 (1 + 0.08)⁵ / (1 + 0.08)⁵ - 1)

A = $200000 * (0.08 (1.08)⁵ / (1.08)⁵ - 1)

A = $200000 * (0.08 *1.4693280768) / (1.4693280768 - 1)

A = $200000 * (0.11754624614 / 0.4693280768)

A = $200000 * 0.25045645456

A = $500912.91

So, the annual payments will be of $500912.91

Loan amortization schedule:

1st year:

Total payment = $500912.91

Interest = $2000000 * 8% = $160000

Principal repayment = $500912.91- $160000 = $340912.91

Outstanding principal = $200000 - $340912.91 = $1659087.09

2nd year:

Total payment = $500912.91

Interest = $1659087.09 * 8% = $132726.9672

Principal repayment = $500912.91 - $132726.9672 = $368185.94

So, at the end of 2nd year, out of total $500912.91 payment made, $368185.94 is the principal repayment.

jeff jeffy answered 7 months ago

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