Finding Annuity Interest Rate (Documentation needed and round totwo decimal place.)Suppose that an insurance...

Finding Annuity Interest Rate (Documentation needed and round to two decimal place.)

Suppose that an insurance company offers to pay you an annuity of $12,000 per year for 10 years in exchange for $82,368.97 today. What is the return on this investment measured in percentage terms? This is an ordinary annuity.

Expert Solution

IRR is the Rate at which PV of Cash Inflows are equal to PV of Cash Outflows.

Year	CF	PVF @7%	Disc CF	PVF @8%	Disc CF
0	$ -82,368.97	1.0000	$ -82,368.97	1.0000	$ -82,368.97
1	$ 12,000.00	0.9346	$ 11,214.95	0.9259	$ 11,111.11
2	$ 12,000.00	0.8734	$ 10,481.26	0.8573	$ 10,288.07
3	$ 12,000.00	0.8163	$ 9,795.57	0.7938	$ 9,525.99
4	$ 12,000.00	0.7629	$ 9,154.74	0.7350	$ 8,820.36
5	$ 12,000.00	0.7130	$ 8,555.83	0.6806	$ 8,167.00
6	$ 12,000.00	0.6663	$ 7,996.11	0.6302	$ 7,562.04
7	$ 12,000.00	0.6227	$ 7,473.00	0.5835	$ 7,001.88
8	$ 12,000.00	0.5820	$ 6,984.11	0.5403	$ 6,483.23
9	$ 12,000.00	0.5439	$ 6,527.20	0.5002	$ 6,002.99
10	$ 12,000.00	0.5083	$ 6,100.19	0.4632	$ 5,558.32
NPV			$ 1,914.01		$ -1,847.99

IRR = Rate at which least +ve NPV + [ NPV at that Rate / Chnage in NPV due to 1% inc in disc Rate ] * 1%

= 7% + [ 1914.01 / 3762 ] * 1%

= 7% + 0.51%

= 7.51%

jeff jeffy answered 1 year ago

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