Mack Aroni, a bank robber, is worried about his retirement. He decides to start a savings account.

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Question:

Mack Aroni, a bank robber, is worried about his retirement. He decides to start a savings account. Mack deposits annually his share of the “loot” which consists of $75,000 a year, for 3 years beginning January 1, 2013. Mack is arrested on January 4, 2015 (after making the third deposit), and spends the rest of 2015 and most of 2016 in jail. He escapes in September of 2016. He resumes his savings plan with semi-annual deposits of $30,000 each beginning January 1, 2017. Assume the bank’s interest rate was 9% compounded annually from January 1, 2013,
through January 1, 2016, and 12% annual rate semiannually thereafter.

INSTRUCTIONS:
When Mack retires on January 1, 2020 (6 months after his last deposit), what is the balance in his savings account?

HINT: This is a deferred annuity problem
1. Calculate the future value of the $75,000 during the annuity period (2013, 2014, & 2015).
2. Calculate the future value of the sum in step 1 for the deferral period (2016-2019).
3. Calculate the future value of the $30,000 annuity during its annuity period (2017 – 2019)
4. Add steps 2 & 3.
5. This is an annuity due because the payment begin at the start date (or end before he starts collecting his retirement).