# A corporation needs to save $14 million to retire a$14 million mortgage that matures in 19...

## Question:

A corporation needs to repay a $14 million mortgage, 19 years from today. To repay this mortgage, the company plans to deposit a fixed amount into an account at the end of each year for 19 years, with the first payment occurring at the end of the first year. The deposit account will earn 11% interest annually. What equal annual deposit must be made into this account over the next 19 years such that the balance in the account is$14 million ?

## Ordinary Annuity:

An annuity is a series of fixed cash flows over a period of time. These cash flows usually occur once per year or annually. Because these cash flows are over a period of time, the time value of money is essential. In order to capture this time value of money effect, a discount factor, or interest rate, is necessary. This interest rate discounts the series of cash flows over time to present value, or compounds the series of cash flows to a future value. For any annuity, the Present Value, i.e. the value today, of the series of cash flows can be determined using the discount factor. Additionally, for any annuity the Future Value, i.e. the value at some time in the future, of the series of cash flows can be determined using the interest factor.

As there are a series of fixed cash flows for a set period of time, we can conclude the the corporation must invest in an annuity. We are given the...

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