# Annuity

1. Loan Amortization Schedule - Val Hawkins borrowed $15,000 at a 14 percent annual rate of interest to be repaid over 3 years. The loan is amortized into three equal annual end-of-year payments.

a. Calculate the annual end-of-year loan payment

b. Prepare a loan amortization schedule showing the interest and principal breakdown of each of the three loan payments.

c. Explain why the interest portion of each payment declines with the passage of time.

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2. Funding Jill Morgan's Retirement Annuity

Sunrise Industries wishes to accumulate funds to provide a retirement annuity for its vice president of research, Jill Morgan. Ms. Morgan by contract will retire at the end of exactly 12 years. Upon retirement, she is entitled to receive an annual end-of-year payment of $42,000 for exactly 20 years. If she dies prior to the end of the 20-year period, the annual payments will pass to her heirs. During the 12 year "accumulation period" Sunrise wishes to fund the annuity by making equal annual end-of-year deposits into an account earning 9 percent interest. Once the 20-year "distribution period" begins, Sunrise plans to move the accumulated monies into an account earning a guaranteed 12 percent interest per year. At the end of the distribution period, the account balance will equal zero. Note that the first deposit will be made at the end of year 1 and the first distribution payment will be received at the end of year 13.

a. Draw a time line depicting all of the cash flows associated with Sunrise's view of the retirement annuity.

b. How large a sum must Sunrise accumulate by the end of year 12 to provide the 20-year, $42,000 annuity?

c. How large must Sunrise's equal annual end-of-year deposits into the account be over the 12-year accumulation period to fund fully Ms. Morgan's retirement annuity?

d. How much would Sunrise have to deposit annually during the accumulation period if it could earn 10 percent rather than 9 percent during the accumulation period?

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#### Solution Summary

The solution explains the concepts of annuities really well. The solution prepares a loan amortization schedule. This can be used by any person who owns a home to understand how much of monthly payments are going towards interest and how much is going towards the actual amount. Then the solution also talks about retirement annuity and explains the retirement problem really well. All the concepts as they relate to time value of money are explained extremely well in the attachments. Overall, an excellent response to the questions being asked.