Question

The Dell Corporation borrowed ​$ 10,000,000 at 5​% interest per​ year, which must be repaid in equal EOY amounts​ (including both interest and​ principal) over the next seven years. How much must Dell repay at the end of each​ year? How much of the total amount repaid is​ interest?

Answer 1

Answer:

- Dell must repay $1,728,198.18 at the end of each​ year.

- $2,097,387.29 out of the total repaid amount is interest expense.

Explanation:

- EOY equal repayment calculation:

We apply the present value formula for annuity to calculate the equal repayment amount Dell needs to make in the next 7 years.

Denote C is equal repayment, PV is present value of the loan which is $10 million, i is interest rate which is 5%, n is the number of repayments which is 7.

We have: C = (PV x i) / [ 1 - (1+i)^-n] => C = (10,000,000 x 5%) / ( 1 -1.05^(-7)) = $1,728,198.18.

- Interest expense calculation:

Total repayment made: 1,728,198.18 x 7 = $12,097,387.29.

Total interest expense = Total repayment made - principal amount = 12,097,387.29 - 10,000,000 = $2,097,387.29