Question

RETIREMENT SAVINGS AND PLANNING Sunrise Industries wishes to accumulate funds to provide a retirement annuity for its vice president of research, Jill Moran. Ms. Moran 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 5 TIME VALUE OF MONEY (TVM) 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% interest. Once the 20-year "distribution period" begins, Sunrise plans to move the accumulated monies into an account earning a guaranteed 12% per year. At the end of the distribution period, the account balance will be zero. Note that the first deposit will be made at the end of year 1 and that the first distribution payment will be received at the end of year 13. Required

a. How large a sum must Sunrise accumulate by the end of year 12 to provide the 20-year, $42,000 annuity?
b. 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. Moran's retirement annuity?
c. How much would Sunrise have to deposit annually during the accumulation period if it could earn 10% rather than 9% during the accumulation period?
d. How much would Sunrise have to deposit annually during the accumulation period if Ms. Moran's retirement annuity were a perpetuity and all other terms were the same as initially described?

Answer 1

To provide a retirement annuity, the sum needed at retirement is calculated using the present value of annuity formula, while the annual deposits during the accumulation period are determined using the future value of annuity formula. Changes in the interest rate and terms of the annuity, such as a perpetuity, will affect the annual deposit amounts required.

Step-by-step explanation:

The question involves calculating the fund's accumulation to provide a retirement annuity and determining the annual deposits needed during the accumulation period. To solve this problem, one requires an understanding of present value (PV) and future value (FV) concepts in finance, particularly as they relate to annuities and the effect of compound interest.

To calculate the sum needed by the end of year 12 to provide the 20-year, $42,000 annuity at a 12% interest rate, we calculate the present value of an annuity:

• PV = Pmt [((1-(1+r)^-n)/r)]

To calculate the required end-of-year deposits, we apply the future value of an annuity formula:

• FV = Pmt [((1+r)^n-1)/r]

If the interest rate during the accumulation period is 10%, the annual deposit would change because a higher interest rate allows for a smaller deposit to reach the same future value. If the retirement annuity is a perpetuity, the formula simplifies to PV = Pmt / r because perpetuities have no end.

Understanding these principles is necessary to provide sufficient retirement savings and engage in effective financial planning.