# Can anybody solve this Question?? it’s so hard~?

# Pension funds

Sharb Digit Pty Ltd wishes to accumulate funds to provide a **retirement pension funds annuity** for its Director of Marketing, Penny Peters. Penny, by contract, will retire at the end of exactly 10 years. On retirement, she is entitled to receive an annual end-of-year payment of $35,000 for exactly 20 years. If she dies prior to the end of the 20-year period, the annual payments from the *pension funds* will pass to her heirs. During the 10-year ‘accumulation period’, Sharb Digit wishes to fund the pension funds annuity by making equal annual end-of-year deposits into an account earning 8% p.a. interest. Once the 20-year ‘distribution period’ begins, Sharb Digit plans to move the accumulated monies into an account earning a guaranteed 10% p.a. 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 11.

Please solve the following for the pension funds question:

1.Draw a time-line depicting all the cash flows associated with the above accumulation and distribution periods.

2.How large a sum must Sharb Digit accumulate by the end of the year 10 to provide the 20-year, $35,000 pension funds annuity?

3. How large must Sharb’s equal annual end-of-year deposits into the account be over the 10-year accumulation period to fund Penny’s retirement pension funds annuity fully?

2) The formula you want is the “sinking fund” formula.

[1 – (1+r/n)^(-nt)]/[n/t]

In this case, r = .10, n = 1, and t = 20.

[1 – (1.1)^(-20)]/[.1] = 8.51356372 so the company needs to have 8.51356372 * 35000 = $297,974.73 in the annuity

3) In order to accumulate that much money, they need the version of the formula for annuities

[(1 + r/n)^(nt) – 1]/[r/n]

[(1 + .08)^10 – 1]/[.08] = 14.48656247

and 297974.73/14.48656247 = $20569.04 per year

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Money deposited like this, especially if you deposit it monthly rather than annually, accumulates quickly.