Question

Your 75-year-old grandmother expects to live for another 15 years. She currently has $1,000,000 of savings, which is invested to earn a guaranteed 7.5% rate of return. Ignoring the effects of inflation, CONSTRUCT the amortization table for the 15 years, if she withdraws at the beginning of each year and keep the withdrawals constant in nominal terms, until the balance reaches a balance zero at the end of the 15th year. LABEL properly.

Answer 1

Sol:

Present value	-1,000,000
Period	15
Rate	7.50%
Annual withdrawal	$105,383.48
Amortization schedule
Year	Opening balance	Annual withdrawal	Principal	Interest	Closing balance
0	1,000,000				$1,000,000.00
1	1,000,000	$105,383.48	$105,383.48	$0.00	$894,616.52
2	$894,616.52	$105,383.48	$38,287.24	$67,096.24	$856,329.29
3	$856,329.29	$105,383.48	$41,158.78	$64,224.70	$815,170.51
4	$815,170.51	$105,383.48	$44,245.69	$61,137.79	$770,924.82
5	$770,924.82	$105,383.48	$47,564.11	$57,819.36	$723,360.71
6	$723,360.71	$105,383.48	$51,131.42	$54,252.05	$672,229.29
7	$672,229.29	$105,383.48	$54,966.28	$50,417.20	$617,263.01
8	$617,263.01	$105,383.48	$59,088.75	$46,294.73	$558,174.26
9	$558,174.26	$105,383.48	$63,520.41	$41,863.07	$494,653.85
10	$494,653.85	$105,383.48	$68,284.44	$37,099.04	$426,369.41
11	$426,369.41	$105,383.48	$73,405.77	$31,977.71	$352,963.64
12	$352,963.64	$105,383.48	$78,911.20	$26,472.27	$274,052.44
13	$274,052.44	$105,383.48	$84,829.54	$20,553.93	$189,222.90
14	$189,222.90	$105,383.48	$91,191.76	$14,191.72	$98,031.14
15	$98,031.14	$105,383.48	$98,031.14	$7,352.34	$0.00

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