Question

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

   
Carol wants to invest money in a 6% CD account that compounds semiannually. Carol would like the account to have a balance of $70,000 4-years from now. How much must Carol deposit to accomplish her goal?

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

  
Today, Thomas deposited $180,000 in a 2-year, 12% CD that compounds quarterly. What is the maturity value of the CD?

Answer 1

Answer 1)

Calculation of amount to be invested to have $ 70,000 at the end of 4 years

Amount to be Invested = Maturity amount X Present value of $ 1 at 3% for 8 periods

Amount to be invested = $ 70,000 X 0.78941

                                          = $ 55,258.70

Therefore amount to be invested today at 6% compounded semi-annually for 4 years to have $ 70,000 at the end of the period id $ 55,258.70

Note: Since interest is compounded semi-annually, the annual rate of interest to be used as discounting factor will be halved (i.e.6%/2 = 3%) and the number of periods will be doubled (i.e.4 years X 2 = 8 semi-annual periods).

Answer 2)

Calculation of maturity value of $ 180,000 deposited in CD for 2 years at 12% compounded quarterly

Maturity amount = Amount Invested X Future value of $ 1 at 3% for 8 periods

                                 = $ 180,000 X 1.26677

                                  = $ 228,018.60                                           

Therefore maturity value of CD will be $ 228,018.60

Note: Since interest is compounded quarterly, the annual rate of interest to be used for future value calculation will be divided by 4 (i.e.12%/4 = 3%) and the number of periods will be multiplied by 4 (i.e. 2 years X 4 = 8 quarterly periods).