Question

Q17 Present and future value tables of $1 at 3% are presented below:

N	FV $1	PV $1	FVA $1	PVA $1	FVAD $1	PVAD $1
1	1.03000	0.97087	1.0000	0.97087	1.0300	1.00000
2	1.06090	0.94260	2.0300	1.91347	2.0909	1.97087
3	1.09273	0.91514	3.0909	2.82861	3.1836	2.91347
4	1.12551	0.88849	4.1836	3.71710	4.3091	3.82861
5	1.15927	0.86261	5.3091	4.57971	5.4684	4.71710
6	1.19405	0.83748	6.4684	5.41719	6.6625	5.57971
7	1.22987	0.81309	7.6625	6.23028	7.8923	6.41719
8	1.26677	0.78941	8.8923	7.01969	9.1591	7.23028
9	1.30477	0.76642	10.1591	7.78611	10.4639	8.01969
10	1.34392	0.74409	11.4639	8.53020	11.8078	8.78611
11	1.38423	0.72242	12.8078	9.25262	13.1920	9.53020
12	1.42576	0.70138	14.1920	9.95400	14.6178	10.25262
13	1.46853	0.68095	15.6178	10.63496	16.0863	10.95400
14	1.51259	0.66112	17.0863	11.29607	17.5989	11.63496
15	1.55797	0.64186	18.5989	11.93794	19.1569	12.29607
16	1.60471	0.62317	20.1569	12.56110	20.7616	12.93794

   
Bill wants to give Maria a $540,000 gift in 4 years. If money is worth 6% compounded semiannually, what is Maria's gift worth today?

Multiple Choice

• $424,886.

• $537,250.

• $426,281.

• $427,806.

Answer 1

Answer)

Calculation of value of Maria’s Gift today

The value of Maria’s gift can be calculated by using present value factor. Since the money is compounded semi-annually, in order to calculate the effective interest rate, the actual rate of interest will be halved (i.e. 6%/2 = 3%) and the number of periods will be doubles (i.e. 4 years X 2 = 8 semi-annual periods)

Present value of gift = $ 540,000 X Present value factor at 3% at the end of 8 periods

                                      = $ 540,000 X 0.78941

                                      = $ 426,281.40 or $ 426,281(rounded off)

Thus the correct answer is $ 426,281.