Question

Present Value and Future Value T he following situations require the application of the time value of money: Use the appropriate present or future value table: FV of $1, PV of $1, FV of Annuity of $1 and PV of Annuity of $1 1. On January 1, 2017, $16,000 is deposited. Assuming an 8% interest rate, calculate the amount accumulated on January 1, 2022, if interest is compounded (a) annually, (b) semiannually, and (c) quarterly. Round your answers to the nearest dollar. 2. Assume that a deposit made on January 1, 2017, earns 8% interest. The deposit plus interest accumulated to $20,000 on January 1, 2022. How much was invested on January 1, 2017, if interest was compounded (a) annually, (b) semiannually, and (c) quarterly? Round your answers to the nearest dollar.

Answer 1

1. Calculation of amount accumulated on January 1, 2022:-
Amount deposited in january1, 2017 = $16000
	Interest is
	Compounded annually	Compounded semi-annually	Compounded Quarterly
Interest rate	8.00% p.a.	8.00% p.a.	8.00% p.a.
Peridic Interest rate	8%	4%	2%
Periods	6 years	6 years * 2 = 12 semi anuuals	6 years * 4 = 24 Quarters
Amount	16000 [(1+ 0.08)^6]	16000 [(1+ 0.04)^12]	16000 [(1+ 0.02)^24]
Amount accumulated on January 1, 2022	$                                25,390	$                                          25,617	$                                                    25,735
Another way using FV
Amount	16000 * FV(8%,6)	16000 * FV(4%,12)	16000 * FV(2%,24)
	16000 * 1.58687	16000 * 1.60103	16000 * 1.60843
Amount accumulated on January 1, 2022	$                                25,390	$                                          25,617	$                                                    25,735
2. Calculation of amount invested on January 1, 2017:-
Amount accumulated on January 1, 2022 = $20000
Let amount invested on January 1, 2017 = P
	Interest is
	Compounded annually	Compounded semi-annually	Compounded Quarterly
Interest rate	8.00% p.a.	8.00% p.a.	8.00% p.a.
Periods	6 years	6 years * 2 = 12 semi anuuals	6 years * 4 = 24 Quarters
P	20000/ [(1+ 0.08)^6]	20000/ [(1+ 0.08/2)^12]	20000/ [(1+ 0.08/4)^24]
Amount invested on January 1, 2017	$                                12,603	$                                          12,492	$                                                    12,434
Another way using PV
P	20000 * PV(8%,6)	20000 * PV(4%,12)	20000 * PV(2%,24)
	20000 * 0.63016	20000 * 0.62459	20000 * 0.62172
Amount invested on January 1, 2017	$                                12,603	$                                          12,492	$                                                    12,434

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