Question

Use the table below to answer the following question:
	Present Value of an Annuity of 1				Future Value of an Annuity of 1
Period	3%	4%	6%	8%	3%	4%	6%	8%
3	2.8286	2.7751	2.6730	2.5771	3.0909	3.1216	3.1836	3.2464
4	3.7171	3.6299	3.4651	3.3121	4.1836	4.2465	4.3746	4.5061
5	4.5797	4.4518	4.2124	3.9927	5.3091	5.4163	5.6371	5.8666
6	5.4172	5.2421	4.9173	4.6229	6.4684	6.6330	6.9753	7.3359
7	6.2303	6.0021	5.5824	5.2064	7.6625	7.8983	8.3938	8.9228
8	7.0197	6.7327	6.2098	5.7466	8.8923	9.2142	9.8975	10.6366
9	7.7861	7.4353	6.8017	6.2469	10.1591	10.5828	11.4913	12.4876
10	8.5302	8.1109	7.3601	6.7101	11.4639	12.0061	13.1808	14.4866

Alicia receives alimony payments every 6 months and the next payment is tomorrow. Median homes go for $650000 and she wants to save $357,500 for 3 years. How much money should Alicia put away into an investment each time she receives alimony payments if she can get a 6% return a year?

$56,147

$53,659

$49,445

$66,872

Answer 1

Formula for FV of annuity due is:

FV = (1+r) x P x [(1+r) ⁿ – 1/r]

Or

FV = (1+r) x P x FVIFA (r, n)

FV = Future value of annuity due = $ 357,500

P = Periodic cash deposits

r = Rate per period = 6 % p.a. or 0.06/2 = 0.03 semiannually

n = Number of periods = 3 years x 2 periods = 6 periods

Substituting the values in above equation and solving for P, we get periodic deposits as:

$ 357,500 = (1+0.03) x P x FVIFA (3 %, 6)

$ 357,500 = (1.03) x P x 6.4684

$ 357,500 x (1.03) = P x 6.4684

$ 347087.378640777 = P x 6.4684

P = $ 347087.378640777/6.4684

P = $ 53,658.92317122890 or $ 53,659

Hence option “$ 53,659” is correct answer.